{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformer Model\n",
    "In this notebook, we show an example of how Transformer can be used with darts.\n",
    "If you are new to darts, we recommend you first follow the `darts-intro.ipynb` notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fix python path if working locally\n",
    "from utils import fix_pythonpath_if_working_locally\n",
    "fix_pythonpath_if_working_locally()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import shutil\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "\n",
    "from torch.utils.tensorboard import SummaryWriter\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from darts import TimeSeries\n",
    "from darts.dataprocessing.transformers import Scaler\n",
    "from darts.models import TransformerModel, ExponentialSmoothing\n",
    "from darts.metrics import mape\n",
    "from darts.utils.statistics import check_seasonality, plot_acf\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import logging\n",
    "logging.disable(logging.CRITICAL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Air Passengers Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will test the performance of the transformer architecture on the 'air passengers' dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read data:\n",
    "df = pd.read_csv('AirPassengers.csv', delimiter=\",\")\n",
    "series = TimeSeries.from_dataframe(df, 'Month', ['#Passengers'])\n",
    "\n",
    "# Create training and validation sets:\n",
    "train, val = series.split_after(pd.Timestamp('19590101'))\n",
    "\n",
    "# Normalize the time series (note: we avoid fitting the transformer on the validation set)\n",
    "# Change name\n",
    "scaler = Scaler()\n",
    "train_scaled = scaler.fit_transform(train)\n",
    "val_scaled = scaler.transform(val)\n",
    "series_scaled = scaler.transform(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "\"the 'air passengers' dataset has 144 data points\""
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "'the \\'air passengers\\' dataset has {} data points'.format(df.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We train a standard transformer architecture with default hyperparameters, tweaking only two of them:\n",
    "\n",
    "* _d\\_model_, the input dimensionality of the transformer architecture (*after* performing time series embedding). Its default value is 512. We lower the value from 512 to 64, since it is hard to learn such an high-dimensional representation from an univariate time series\n",
    "* _nhead_, the number of heads in the multi-head attention mechanism. We increase the value from 8 to 32. This means that we compute multi-head attention with 32 heads of size _d\\_model_/_nhead_=64/32=2 each. This way, we obtain low-dimensional heads that are hopefully suitable to learn from univariate time series\n",
    "\n",
    "The goal is to perform one-step forecasting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "N_EPOCHS = 1000\n",
    "NR_EPOCHS_VALIDATION_PERIOD = 10\n",
    "\n",
    "# Number of previous time stamps taken into account.\n",
    "SEQ_LENGTH = 10\n",
    "# number of output time-steps to predict\n",
    "OUTPUT_LEN = 1\n",
    "# Number of layers in encoder/decoder\n",
    "NUM_LAYERS = 6\n",
    "\n",
    "my_model = TransformerModel(\n",
    "    batch_size = 32,\n",
    "    input_length = SEQ_LENGTH,\n",
    "    input_size = 1,\n",
    "    output_length = OUTPUT_LEN,\n",
    "    output_size = 1,\n",
    "    n_epochs = N_EPOCHS,\n",
    "    model_name = 'air_transformer',\n",
    "    log_tensorboard=True,\n",
    "    nr_epochs_val_period = NR_EPOCHS_VALIDATION_PERIOD,\n",
    "    model = None,\n",
    "    d_model = 64,\n",
    "    nhead = 32,\n",
    "    num_encoder_layers = 6,\n",
    "    num_decoder_layers = 6,\n",
    "    dim_feedforward = 2048,\n",
    "    dropout = 0.1,\n",
    "    activation = \"relu\",\n",
    "    custom_encoder = None,\n",
    "    custom_decoder = None,\n",
    "    random_state=42,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "37342ac7a07949c68ce125f7cb622966"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "my_model.fit(training_series=train_scaled, val_training_series=val_scaled, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the predictions on the validation set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, by using the \"current\" model - i.e., the model at the end of the training procedure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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N2c/Pz+fToiSUhRBCnFbq6+sZNWoUwcHBA85JKAshhDjtVFRU0NnZ6ZNnW0ZeK8rAjYp8vX2jhLIQQgivqqysJDc3l3/9618+eb6t6VAWvt6+UUJZCCGEVz3wwAO0tLRQXe2BvXrtMFwoS01ZCCHEaWHDhg289tprhIeH+yz8bG3baOHrPmW3bN0ohBBCDMdkMnHnnXdyySWXEBAQQENDg0/KUV9fT2Jios1zUVFRPt0QSGrKQgghvOLll19m9+7dLFu2zKfNxNKnLIQQ4rT329/+lv/5n/8hOzt7RIey9CkLIYQ4pbW3t1NRUcGFF14I+Db8hgplX/cpSygLIYTwuLq6OgBiY2MB34Vyd3c3jY2NQ9aU29vbaW9v93LJzCSUhRBCeJwllMeOHQv4LpSPHj2KpmlDhjLgs35lCWUhhBAeV1tbC5wI5TFjxtDS0kJXV5dXyzHYutcWvt4pSkJZCCGEx9XV1REeHk5QUBDguxqpZRpW/x2iLHy9p7KEshBCCI+rra211pLBdzXSwbZttLCEsjRfCyGEOGXV1tZaB3mB70K5urqamJgYAgJsr52l0+kIDQ2VmrIQQohTV11d3YioKVdWVpKQkDDkNb6criWhLIQQwuP615QDAwMJDg6WUO5HQlkIIYTH1dXV9QllMIeft9e/7h3Kq7dpjP8vE61tWp9rIiMjpU9ZCCHEqav/QC/wTY3UEspdRo2lyzRKK2HDnr7XSE1ZCCHEKa2mtpZ/bb+aLXtP1Ep9GcrPvwdltZAaD9/s7FtTllAWQghxymptbaVNS2T7wSTe+cZ3oWw0GqmpqSE4Mo3fvqzx4M0KV8yGNdv7XiehLIQQ4pRVV1cHEecCsHbXieNjxozxavjV1tZiMpl4b9sMosPhvv+CH0xT2FoELcdP/LIgfcpCCCFOWeZQnkfYaBPbDCcC0Ns10srKSgiezMdbo3l6qULQKIW5+WDshu969StLTVkIIcQpq6amFiLm8d9XQXc3bCwwH/dJKEddSNJYWDjHfCw6QiFvPHyzw7d93RYSykIIITxqz/52GJXADef5Mykd1u7yXU05KGYWUzMVFEWxHv/BNPhm54nroqKiaG5uxmg0eq1sFrbXGetFVdUI4GtgInCmXq/f0+ucP/AikAVs0+v1d3mqoEIIIU5OWw0h+JmayBsfydz8E/3KvghlJeRc8jP7Hj93msLz72s0H9cIC1as6183NTUNupuUp9hTUz4OXAq8a+PcZUClXq+fA4SoqnqWOwsnhBDi5Le3ciyRyh78/RXm5StsLoT2Do2oqCivbt9YfriGdv90pmYqfY7PzQeTCb773vy9ZQlQby9sAnaEsl6v79Lr9XWDnD4b+Krn6y+A2e4qmBBCCPfYs2cPmzZt8smzNU3jUGMaiaH7AJiTDx2dsLXI+9s3Gsr90dANqCmPCe/br5ycnAzAoUOHvFKu3oZtvh5GFHCs5+smYMBeWKqqLgGWACxatMjFx50e2tvbMRgMvi7GiCbvyD7ynoZ3qr8jTdO44YYbiIiI4JVXXnHqHq68o4M1Otq6U4kfXWy9R2psCu+tauaiXHMYb9++nfT0dKfu74jS2lB0ke0YWyro/3GmpsXw+cYgbjuvAjBP19qwYQMpKSl233+w95SdnW33PVwN5UYgvOfrCGBAXV+v168AVgAYDAbNkcKdrgwGg0N/iacjeUf2kfc0vFP9Ha1atYq9e/cyffp0pz+nK+/o22INf+0YZ0waZb3H+aqJgopofnnzdAAiIiK88nfQ2JVGSnQTEyYMfNZVP9B4bY3GuKQswoIVsrOzaWlpcahc7vh3ydXR1xuAC3q+ng985+L9hBBCuNGTTz6Jn5+fzxbD+GaHhq5tE3GxMdZjc/MVNhRAaJj3tm/s6Oig3T+LnKQOm+fVCebpWnsPmr8fP348+/fv93i5+rMrlFVV/Qy4CHhRVdXFqqou7zn1CZCiquo6oF2v12/0UDmFEEI4aNeuXXz55Zf88Ic/9Ekoa5rGt7vAeGRVnx2i5uZDaxsUHNQREhLilVCuqqqGkHymZduOvYQYCAuGwp5uZF+Fsl3N13q9/pJ+h17pOW4EFru3SEIIIdzhqaeeYsaMGSxcuJDXXnsNk8mEn5/3lqdobYPDdUDTNmJjL7YeTxsH46Jh017vTYvaVXgEdNOYnW/7lxNFUchN1dh7UAMUxo8fT2lpKZqm9ZnT7GmyeIgQQpyCysrKePPNN7n//vuJiorCZDLR0tLi1TLUW4YBd9X32bZRURQmpUPhIc1roby5oA00E+dMixz0molpfWvKzc3NHDlyxONl601CWQghTkF/+9vfSEpK4pprrvH61COL+qaeL7rq+zRfA0xIgaIy79WUvy/1I8B4gLCQwWMvN1XpE8qA15uwJZSFEOIUtGPHDhYsWEBAQIB1hSqvh7KlptzdMGBlrNxUhaJD3gvlfVUhhPsdGPKa3FQorYS2Do24uDhCQkIklIUQQriurKzMOsfWEsre3mSh/hjo/I3ERAXj7+/f59yEFKhugODwBK+Uq/JYDPFhtUNeMzENNA0M5eYm9oyMDAllIYQQrtE0jfLycuvKVGFhYSiK4pPm69EBbQOargEmpJr/qQVlezyUW9s0jnXFkR57bMjr0uJhVKBvR2BLKAshxCmmsbGR1tZWayj7+fkRGRnp9VBuaIZAv+Y+g7wsxkWbpyB1+Kd7PJS/LwXwY1La0Ls++fsrTEihZwS2hLIQQgg3KC8vB+izRKQvQrm+ScPf1Gizpqwo5gBs7k70eCgXHADFeJQJ6eHDXpubeqKmLM3XQgghXFZWVoaiKCQmJlqPRUZG+qRPWes3Haq3CalwtD3W4+UqKe9CayslMTFh2Gv7j8Curq6mtbXVo+XrTUJZCCFOMeXl5cTFxREYGGg95puaMnS319qsKQNMSFGoORbp8e0bDYfaoKOMhIThQ3limnmgl9GoWadFlZaWeqxs/UkoCyHEKab3IC+LqKgon0yJ6mitGrSmnJsKVY3BoAR4tLZ8oMpkdyjnpkKXEfZXQmpqKv7+/hLKQgghnNd7OpSFT2rKx+D4sfLBm69ToNvkB0GZHg3lw0f88Dceti6iMpSsJPD3N/cr63Q6UlJSvNqvLKEshBCnGFs1ZV/0KR9pNGFqryMpKcnm+fGJ4O+nQfAEj5Wto8NI3bEg1Cmxdq1hHahTyEz03W5REspCCOFGhw4dYv369T4tw2Ch7M2astGo0dTqB8Z6UlNTbV4TqFPISABG53gslP/8/Oug6Hjwnpvt/hnzCGzfTIuSUBZCCBd1dnby6KOPMn36dNLS0pg7dy7Nzc0+KYvJZKKiomJA87W3+5Qbe/a+COAY8fHxg16Xm6oQED7ZI6Hc0NDAE8veAOCsacP3J58ok+8WEJFQFkIIF73xxhs8/vjjnHvuufzjH/9A0zQqKyt9Upaamhq6urp8XlO2rHudGBs05HaRE1JACcn1SCj/+te/JiAkg6BAjbGDbw41wMQ087Qok8k8AvvgwYMYjUMvPOIuEspCCOGioqIi8vLy+POf/8w111wD4LNQtiwcYiuUjx07Rnd3t1fKYdkhKjUxbMjrJqQqdI/KoqZm6HWpHbVnzx7+7//+j/lX/oSUOMWhPZFzU+F4O5TXmmvKRqPR+l49TUJZCCFcZDAYyMnJAczrTIeEhPgslMvKytDpdAOajC2bUjQ1Ndn6Mbez1JQz06KHvC43FUxKKIaDQ69L7aj//Oc/ZGZmEhmXT2qcYz+bPs78z0PVWPvDy8rK3Fq+wUgoCyGEiwwGA9nZ2YB5+ciEhASf1pQTExMHNBl7e0/l+mPgZzpGelrykNfl9HR9lxz2H/I6RxUXF5OXl0d5LaQ4GMpRYRAcZK4pR0REEBgYSE1NjVvLNxgJZSGEcEF3dzclJSXWUAZ8Hsr9m64Br++pfKRJQ+s6Qlpa2pDXRYUphI5qpaIh1K3PLyoqIicnx1zbjbe/6RrMv1glx5pDWVEU4uPjJZSFEOJkUF5eTkdHx4gK5f4jr8H7oXy4pg2to27Q6VC9xUe20dASiqZpbnm2pmnWLoWyWhxuvgZ6Qtlcnri4OAllIYQ4GRgMBgCysrKsx3wZymVlZTZrysHBwQQEeHY5yz7lqGwFY8OwNWWAxBgFo38cDQ0Nbnn24cOHaW1tJSFlIsdaHW++Bqw1ZZBQFkKIk4bBYCAhIYHQ0BPNr76uKdsKZUVRvDpXuepIB0r3UbvWm05PDITABLeNcC4uLgYgKMLceuF0TbnO/LWEshBCnCR6j7y2sISyu5pj7dXZ2Ul1dbXN5mvw7lzluqMmwoI68fcffgBXdmoIjEp0ayjHxcXR0BqKokCi7aW3h5Qcq0hNWQghTja9R15bJCQk0N7e7vUNIA4fPoymaTZryuDdUG5s8WNMhH3XpsT5o4xK4tAh90w7Ki4utg7ySogxL+fpqORY81zr4+0acXFxVFdXu6Vsw5FQFkIIFwwWyuD9BUQGWzjEwpubUrR0jCJuTIBd1yaOBc0vmH0H69zy7OLiYiZMmEBZrUaK7a2ch5Xc83MVdSdqyt5o+ZBQFkIIJ7W3t3Pw4MERFcohISGDblHozZpyhymUpLhgu65NjDH/s6TsuFue3bumnDr4sttDsoRyea05lDs6Ojh2zL0LnNgioSyEEE7av38/mqYNCOXg4GAiIyO9HsqWkdeDLSnprYFex9s1NCWI9KShl9i0sPT5HqrqcvnZbW1tHDp0yDodytmacliwQkQoVPSEMuCVfmUJZSGEcJLBYCAgIID09PQB53wxAnuwkdcW3qopH6gw1ygz04deYtMiOEhhtK6d6gbXV/Xat28fmqY5vXBIb8ljT9SUQUJZCCFGNIPBQEZGBjqdbsA5X4RyRUXFsKHsjT7lgmLzoKiJmfZXU2PCOznaOtrlDTOKi4vR6XSMS0ijqt65OcoWlgVEoqKi0Ol0EspCCDGS2RrkZeGLUK6urh5y72Jv1ZSLS80DtibljLP7ZxKiNUy6cS6Pci4uLiYzM5Pqo+ZatzNzlC16L7Vpa1rUzTffzIYNG4a8h8nk2OAwu0JZVdU/qqq6TlXVf6mqqut1fLSqqh+rqvqtqqqrVFV14eMLIcTJZaSFck1NjbWp1RZv9SmXljeB1klUuH2jrwHSEwIh0PW5ypZBXmU9+elaTXnwucqNjY38+9//pr29fdCfb+/QWPiQm0NZVdV8IFGv188BioBre52+GNij1+vnAa8AP3bo6UIIcRIbSaGsadqwoRwZGcnx48fp7Oz0aFnKKo+jU5od2sN4fPJolCDXQ9myEcXBaogIhYhQF/qUh1jVy7JqWP+FYyxa2zQuf1BjQ4Fjz7Snpnw28FXP118As3ud2weE9HwdBRxx7PFCCHFyamxspLa2dshQrqqqwmQyeaU8zc3NdHR0EBs7eD+utzalqD7SSbCuzaGfSYpV8AtKdmnfYk3TKC4uJjs7h79/ojEnz+lbAeZQbmqB5uMDFxApLi4mNDTU5jKizcc1Lr5f4/tS+PYvjv1SYE/bQhRQ1fN1EzCm17kSYKKqqgWAApzR/4dVVV0CLAFYtGiRQ4U7XbW3t1sXuRe2yTuyj7yn4Tn7jnbv3g1AQECAzZ83Go10dXWxZcsWxowZM+C8ux08eBAwTwka7PNYBnnt2LHD5ojxwTj6jmoauggeM3g5bOoIptsvnp27Cpz+d7auro5jx46xpyqTjQUaH/6mHIPB+VYB43EdkMq6LQfR6XQcOnTIWraNGzeSmppKSUmJ9fr29nYK9hq49alEKusD+Oe9lei6ugDbv7jZYk8oNwLhPV9HAL238VgErNfr9b9VVfVa4H+BB3r/sF6vXwGsADAYDNpgv1WKE4ZqEhNm8o7sI+9peM6+o61btxISEsI555xjs5l21KhRAIwePdorfwe1tebOz1mzZhEdbXsqUkSEed3LqKgoh8rk6Dtqad/GxOhAsrPtD/4WTQNF48gxndPvq6qqCpQAPtx9JosvVrj8vDSn7mORnKoBGv7BaeTm5vLVV19Zy1ZXV0d+fn6fshoMBl5alUlJJWx7USEr2f7Pb2FP8/UG4IKer+cD3/U6p3CiyfoI5tAWQohTnmX60WD9ppZR0N7qV92NZd8AACAASURBVK6pqSEgIGDQ1bzgRCh7svm6qamJju4Q4mIGThMbijsWECkuLiZk/F1U1vvzu9uc70u2GD1KISbixFzl3kttWgaU9ba+YDR/egNeuFchK9m55w8bynq9fidQo6rqOmAS8B9VVZf3nP43cJmqqt8AjwJ/dqoUQghxkhlu+tGoUaOIiYnxaijHxsbi5zf4/9aDgoIICgry6FzltWvXgi6anAz7Fg6xGBsJ/n7dVNYPH2bbtm1j/fr1A45v3V5E57hfcvf15j5qd0jqmascFxdHW1sbLS0tdHd3U1JS0ieUaxo0HngpjsUXw00XOv9su8ar6/X6+/sd+mnP8SZggdNPF0KIk1RVVdWQoQzeHYFdW1s75CAvC0/PVf76668JCruHhLFBDv2cn59CdGgHtW0hdHR0WJv/++vs7OT6668nMjKSbdu29Tn3yfZ0AkIDeeAm9wQy9FrVa9aJVb38/Pzo6OiwhvKxVo2bfqcRFmziuZ+79mxZPEQIcVLRNI2//e1vHD582KflqK6uZty4oRfH8GYoDzcdysLTc5VXrlyJoosmOnz4a/tLiAECE4f8u12xYgWlpaXs2LGjz+c4Un+Mar+rWDir0qVpUP1ZFhCx/AJWU1NjnQ6VlZXFtmKN6bdrFJfDsz+rJjRYQlkIcRqprKxk6dKlXHXVVUMu3OBp9tSUExMTR1woe7KmXFFRQWFhER3dwUQ7McIobZwORiUOOi2qpaWFRx99lKVLl6IoSp8m7D+/ehACYnj4x07uQDEIywIiUVFRBAQEWEM5OTmZf34VzNn/rZGTDDtfUshJcn3+t4SyEOKksnfvXsC8Q9Mdd9zhlT1ubTlZa8qeXP961apVBEWMx6QpxEY6/vOpCTr8RicPuoDIsmXL6Orq4rHHHmPq1Kl8++231nOvrY4gvPMrJmYOPtDNGb2X2oyNjaW6uto8RznzLpYu03jsdoWP/6AQE+me2rmEshDipLJ3715SUlJ4++23efXVV/nrX//q9TIcP36cY8eOjag+ZctAr+G4s6bcfz7xypUrGT/z/xEWDOoEx++XFKMQEJxis6ZcV1fHk08+yUMPPURkZCTnnnuuNZS3FWuUNyUzL+t7pz7HUJJj4Xg7NLacGIG9sTCUIuP/8IefKtx/o4Kfn/uayyWUhRAnlb179zJx4kTOP/98nnzySe6++2527drl1TJYVnayp6ZcXV3t8s5H9qitrfVqn/KePXvIycnhgw8+AMx9/StXrkSLvIyLZ0GgzvGgShwLRv94SksPDDj39NNPExERwdKlSwGYN28e27dvp7m5mb+8a8Lv+HYWnj9wdS1Xpfb83nXvXzV0Meez91AAu40Pc2Z6Eb+4ye2Pk1AWQpxcLKEMcPfddzN27FjzNBwvqqoyL3JoT03ZZDK5vPPRcNra2mhubrYrlKOjo60LjbjCsoLY0qVLaWpqoqCggOraZvbVp3LlOc7VHBNjwMQoCkuqBpxbv349119/PaNHjwZgzpw5mEwmPv1qC2+u0jCV/4Vzzpk94OdclRqv8H/3KnxfClva/8i7pb9Ca9rEw/9V7dDa3vaSUBZCnDQ0TaOgoMAayoqiMH78eA4cGFiz8qTq6mp0Ot2wy2cmJSUB5gFQnmTZKMGeUB4/fjz79+93uS++qqrKupb2Aw88wNdff01E2rV0a35cfKZz97QsILKvfOC62f0X64iKimJK3nR+/0Y4o/zbidZWkZWV5dyDh/GzKxW2rvBjybQ/EXjo/0HhdUyeZHsjClfZv6+WEEL4WE1NDUePHrWGMkB6errXQ7mqqoq4uLghF+oAiI2NRafTUV5ezqxZszxWHkdCOSsri2PHjlFXV2dXH/RgKisrSUtL4ze/+Q1XXXUVGRkZjMn6BzMmQFSYczXIhBjzP+sadbS2thISYt7vqKGhgSNHjvRZ0rLqiMaRcW9QUxPPObEvEHGW6pGaa285qYF0lv0fo0ePtv7C5W5SUxZCnDQsI69zc3Otx3wRyvaMvAbw8/MjKSnJ5e0Ih1NTU4OiKMTExAx7bWZmJgD79u1z6ZmVlZWMGzeOhQsXcu2111JaepC67plON12DeVnLyJBuGJXI/v37rcctmz5YQvm7781zg/1GjYWdZ1KyaRlnn322S5/HHpZferKzs4f9hcxZEspCiJPG3r17SUhIsDabwolQ9ubUKHvmKFskJw8+xcddamtriY6OJiBg+MbPsWPHEhYW1md3I2dUVVVZty187rnnOGvBfbR0BHGFi926SXF++I1O6VM+g8FASEgI48aN47ONGhfcrTEnH9Y9Z6S7ZS+VlZXMnu3+/uT+LKE82B7K7iChLIQ4afQe5GWRnp7OsWPHPLqec3/21pTBO6Fs7xxlMPfDZ2VluaWmbAnl+Ph4Zl/+BHnjIW2ca03I07IUgmLn9SmfZZeqt1fDlQ9p/PhSePM3CmnJMUyaNAmdToeqqi491x6WX8QklIUQgsFDGaC0tNRr5XCkppyUlOSVgV72hjKYm7BdrSlbmq/BPADvw/W4XEsG+ME0hY5RMyk2nPj7NBgMjEr+ETf+TuOBm+C5u07MDb7ooos4++yzCQpybK1tZ0hNWQgherEVyomJieh0Oq/2K4/EmrIjg7ZcrSl3d3dTU1NjrSnvMEBJBSyc4/pAq/OmQzfB7Nx3Ip4MBgP7Oq7nZ1fCYz/x6zOg6/e//z0ffvihy8+1R0xMDA899BDz58/32DMklIUQJ4W6ujrq6uoGhLK/vz+pqaleC2VLIDnSp1xVVYXRaPRYmZytKTvbD19bW4vJZLKG8rJ3NM7IhenZw/ygHVLjFaJDmth3JAUw18KLDsGR42NZvGBg6AcFBVn3ifY0RVF4/PHH7RpQ5ywJZSHESaGwsBBgQCiDd0dgHzlyBJPJ5FBN2WQyeXS5TXtX87KwTIs6cuSIU8+zfJZx48ZRUavx5iq453rFbVOS1Mxmmv1m0NrayuHDh2kPuZCx4Z1OLd15spFQFkKcFPbu3UtsbCzR0dEDznkzlO1dzcvCMp/Vk03YztSUAaf7lauqqlAUhbi4OJ5/TyMhBq6Z59StbLpoViCEz6awqNS8vnb0lVxxDm5dY3qkklAWQpwUeq/k1Z83Q9myZKa9oRwTE0NQUJDHBnt1dXXR0NDgUCjHxsYSFhbmdL9yZWUlsbGxdHQFsPwj+Pm1CgEB7gvMay+IAf/RfP5dA1t2VkD4Wdxw/ii33X8kkxW9hBAnBVuDvCzS09M5ePAgJpPJY4s6WFRVVREVFcWoUfaFhKIoHl1AxLKOtSMDvRRFcWkEtmXk9cufQ7cJfnypU7cZVEp8ADrjPr7d5YfWMRp/rZl5U8Pd+5ARSmrKQoiTwlChnJGRQWdnp7Vp2ZMcGXlt4ckR2I4ssdmbKyOwq6qqGDcuiWfe0fjJZRAR6v5m5figIgoqxvL94XRSw/c6tevUyUhCWQgx4jU2NlJdXd1nec3evDlX2ZE5yhaeDGVnaspg7ld2pfm6M3w+B6vhf67xTFhOTqqlpi2NOuNkzsqq8cgzRiIJZSHEiHfo0CHgRPj2Fx0dTWhoqFf6lZ2pKXuy+bqmpoaIiAiHF8/IyspyelpUVVUV+48v4MrZrq/gNZhz8rrRCARN49Kz/T3yjJFIQlkIMeKVlZWhKAqJiYk2zyuK4rXBXiOtpuzowiEWmZmZNDU1UV9f7/DPHqoL4WBjhsdqyQDTJydD625oXEX+5PEee85IIwO9hBAjXnl5OfHx8QQGBg56jbdC2dk+5ZqaGjo7O4f8DM5wdDqUhWXv4ZKSEocWw+ju7uZI4A2kxBzj3GmeW7QjMzMTDDeCqZnx43d57DkjjdSUhRBDamhooKWlxadlKC8vJzk5echrRnpNGeDw4cNuL4+zoRwbG0toaKjD/cr7DtZB7A+56dyjHt2/ODU1Ff+2HaTHddo90v1UIKEshBjSrbfeypIlS3xahvLyclJSUoa8JiMjw+Oh3NLSQmtrq1M1ZXBtAZHS0lI6OjoGHK+qqnIqlC27RTk6LWrFh52gGfnRpZ4NSp1OR3p6unUP5dOFhLIQYkiFhYX85z//oaGhwWdlKCsrs6umXFFRQWdnp8fK4ehqXhaRkZEEBwe7FMo/+MEP+NWvfjWgPGvXrmXOnDlO3dOeEdhGo5G9e/cCYDJpvPFNFNS8Qkaq4/3YjpozZw7nnHOOx58zkkgoCyEGZTQaKSsro7OzkzfffNNn5bC3+VrTNMrKyjxWDstqXo7WlBVFcWmwV0tLC2VlZSxfvpzGxkbr8eXLlzN27FiuueYap+5rT0353//+N9dccw3l5eWs3g7VjcFEd75FQIDnhyT94x//4OGHH/b4c0YSCWUhxKAqKiowGo3MnDmTV155xSdl6O7u5vDhw8OGclpaGuCeucqHDh1i27ZtA45XVVURGBhIZGSkw/dMTk52eqlNS3AajUaWL18OQGdnJy+88AJ33HEHOp3OqftmZGQM+74+//xzTCYTb775JudNh9vVv5Mytsup54nhSSgLIQZl6aP93e9+x9atWykoKPB6GWpqaujq6hq2Tzk0NJSxY8e6pV/5iSeeYO7cuXz//fd9jm/cuJGEhASnBji5UlMuKSkhMDCQe++9l2eeeYaOjg7eeecdjh496lJ/f0ZGBg0NDTQ1Ndk8393dzddff82YMWN47bXXzBtCtGxzuKVA2E9CWQgxqNLSUqKiopg/fz45OTk+qS1bgmy4mjK4bwT2oUOHaGtrY+HChda+9OXLl/PMM8/wyCOPOHVPVxYQKSkpYfz48dx55500Njby+uuv89xzz3H99dc7NcjLwrIYy2DvbPv27dTX1/PQQw+xe/du9uzZQ1VVlXUfZeF+doWyqqp/VFV1naqq/1JVVdfv3H+pqrpaVdVvVFU9yzPFFEL4woEDB8jIyEBRFBYvXsy//vUvurq823RZXl6OTqezK3zcNQK7rKyMe+65B03TuPHGG3n77be54447eOqpp7j11luduqcrNWWDwUB2djaxsbEsWrSIX/7yl2zevJk777zTqftZJCUlERAQMOg7+/LLL0lPT+eyyy4jMzOT119/3boZhfCMYUNZVdV8IFGv188BioBre51LAK4Eztfr9efq9fqNHiupEMLrSktLrbWpW265hbq6Or788kuvlqGsrIykpCS7dn9yR03ZMlgsPz+fDz74gPXr13PDDTdw//33c++99zp93+TkZI4cOUJbW5vDP1tSUmJd7OPee+/lyJEjzJo1i5kzZzpdHoCAgABSUlIG7Vf+4osvWLBgAYqicPPNN/P6669z+PBhqSl7kD015bOBr3q+/gKY3evcAqAD+LqnFh3q5vIJIXzIUlMGSExM5IILLuCtt97yahnsGXlt4Y5QbmxspKWlhZSUFPLy8njnnXd45JFH+MMf/uDSfS194s7UlnuHclZWFk888YTL5bEYbLBXU1MTmzZtYv78+QDcfPPNlJeXU1NTI6HsQfaEchRwrOfrJmBMr3NxQAxwIbAR+H9uLZ0Qwqd615QBZs+ezfbt271aBkdD+ciRIzQ3Nzv9PMuUKkuIXnLJJfz61792efUqSzeAwWBw6OeOHj3KkSNH+iyi8cADD3Duuee6VB6LwX6RWbVqFYqi8IMf/AAw/zJwxhlnAI5PCRP2s2eiWSNg2V06Amjod26NXq/XVFVdBQyYUKaq6hJgCcCiRYtcK+1por293eH/cE838o7s48p7On78OLW1tQQGBlrvERMTQ3FxMd9//73Xlj4sKSnhzDPPdOhzrFmzhgkTJth1bf93tHHjRhRFobW11e3/jiUmJrJ+/XqHVqnavXs3AP7+/h75dz48PJyioqIB937rrbeYPn061dXV1nd04YUXsmXLFtra2uS/PxsG++/Nkb9ve0J5A3AP8CowH/iu17nvgPt7vp4KDGgD0ev1K4AVAAaDQTvdlkxzhmVQhxicvCP7uPKe9uzZA5hXVbI0nQYGBrJ06VI6OzuZMmWK28o5lNraWqZOnWrX50hPT8fPzw9N0+z+3P3f0cqVKxk3bhyTJ092usyDmTx5Mg0NDYOWbefOnTz++OM89thj5OTkALB161aCg4M555xzPLLW9MyZM3n++efJzMy09ttrmsamTZv42c9+RnZ2tvUdPfDAA8TGxjJnzhyPrnt9snLH/5eGbb7W6/U7gRpVVdcBk4D/qKq6vOfcbqBcVdVvgNuA51wqjRBixDhw4ACKopCammo9lpqaSkREBLt2eWfXns7OTmpqauxuvtbpdCQnJ7vUr1xWVjbsnGhn5eTkUFxcPOB4S0sL9913H6qq8t577/HPf/7Tes5gMJCZmemxEMzIyKCjo8O6hChAcXExZWVl1v5ki7CwMO68804JZA+ya500vV5/f79DP+117iG3lkgIMSKUlpaSlJTUZ6tBRVHIy8uzNql62uHDh9E0ze5QBtcHe9mzzrazcnJyBixX2tHRwfTp0zl69Cgvv/wyu3fv5tNPP+X3v/89YG6+92SrUO+5ypb9qleuXElMTAxTp0712HOFbbJ4iBDCpt4jr3vLz8/3Wk25/6Are7gjlD1ZU66pqemzgtauXbsoKSlhw4YN3HLLLVx66aXs3r3buiRn75HXnhAdHU1YWFifEdjr169nzpw5dk1DE+4lb1wIYVP/kdcWllDWNM3jZSgvLyckJMShtaZHeigDfZqwt27dytixY8nMzATMI9zDw8P57LPP0DQNg8Hg0VBWFKXPO9M0jXXr1jm985RwjYSyEMKmoWrKR48edXpzBUdYpkM50odpCRhnfmkwGo0cPnzYY6GckJBAaGjogFCeOXOm9TPqdDouuugiPvvsM+rq6jh27JjHBzWmp6dba8oHDhygsrJSQtlHJJSFEANomjZoTXnSpEn4+fl5pQm7vLzc4YBMT0+ntbWVI0eOOPy8yspKTCaTx0JZURSys7NthnJvl156KStXrrSOgPdkTRn6Lk+6bt06QkJCpD/ZRySUhRAD1NXVcfz4cZs15eDgYLKysrwSys4MurKU2ZktHC2rbXkqlMHchF1UVARAc3MzhYWFA0J5wYIFtLa28ve//53w8HDGjh3rsfJA35ryunXrOOuss7yyX7IYSEJZCDGA5X/QtmrK4L3BXo6s5mURHx9PUFCQU/3KZWVljB49mujoaId/1l69p0Vt374dTdMGhHJ8fDyqqvLOO++QnZ3t8SlIGRkZVFZW0t7ebh3kJXxDQlkIMcCBAwcICgoiPj7e5vmRHMqKopCWluZ0KDvah+2onJwcSkpK6O7uZuvWraSkpBAbGzvguksvvRSj0ejxpmsw//KlaRp6vZ7i4mIJZR+SUBZCDGDpTx4snPLz8ykpKaG1tdVjZWhpaeHo0aNONSU7OwLbkyOvLXJycujo6KCsrMxmf7LFJZdcAni+PxkgLS0NgFdffZWAgABmzZrl8WcK2ySUhRADDDby2iI/Px9N0ygoKHD5WRUVFVx++eWsXbvWeqy5uZnFixej0+nIzc11+J4jOZQtI6mLi4vR6/WDhrKqqkyePJmzzvL8NvXBwcHEx8fz9ttvM2PGDIKDgz3+TGGbhLIQYoDBRl5bJCYmMmbMGLc0Ya9evZpPPvmEefPmcdttt7F+/XpmzpzJxo0b+fbbb62rTDnC3lB++OGHefXVV63feyOUQ0JCSEpKYuPGjZSWlg4ayn5+fnz//fcsWLDAo+WxyMjIoKmpSZqufUxCWQgxwL59+6yLWdiiKIrb+pULCwtRVZWPP/6YVatWMWfOHMaNG8f27dudriVmZGRQVlZGd3f3oNe88847PP744yxbtozGxkbAuSlYzsjJyeH1118HYMaMGR5/nj0sv4RJKPuWhLIQoo+2tjbKy8uHDGXAbWtgFxYWkpuby2WXXcbevXt5//33+frrr4mLi3P6nunp6XR1dXH48GGb58vLy1myZAk//elPCQwMZPny5TQ3Nzvdh+2onJwc9u/fT05ODhERER5/nj0s3RWzZ8/2cUlObxLKQog+LNOhhhtgNHnyZAoKClxebtMSymBu2l24cKHLc2QttT5bc5W7u7u59dZbSUlJ4ZlnnuGmm27i2WefZd++fYBn5yhbWPZ6Hqzp2hfmz5/PT37yE49OBxPDk1AWQvSxb98+/Pz8rCNyB2PZG7i6utrpZ3V0dLB//36nBnMNJTIyksjISJv9ysuWLWPTpk38+9//JigoiB/+8IccPXqUJ554AoCkpCS3lsUWyxrYqqp6/Fn2mj17NitWrPB1MU57EspCiD727dtHWlpany0bbZk4cSKAdSlIZ1jm67o7lME8ytmyclZv//znP/n5z3/OpEmTAPMuSYsXL+add95h7NixjB492u1l6W/SpEn4+/tLU7EYQEJZiBGksLCQxx9/3Cs7MA2mpKRk2P5kgPDwcFJSUlwK5cLCQnQ6HePHj3f6HoPJy8sbMBCto6ODoqKiAfNw77nnHhRF8UrTNZhHrx86dGhE1ZTFyCChLMQI8tZbb/Hwww/7tBlx3759di9YYelXdlZhYSHZ2dkeWWfZ1ujwwsJCjEYj+fn5fY5nZWVxww03WGv/3uDMVC9x6pNQFmIEKSgoIDQ0lLvvvttm06s32FtTBnMou1pT9kTTNZhDubq6mtraWuuxXbt2ERYWZrO//NVXX+Wll17ySFmEsJeEshAjyJ49e7jvvvuYMWMGN910Ex0dHV59fnt7u13ToSwsNWWTyeTU8zwZynl5eQB9asu7du0iLy8PP7+B/+vT6XTodDqPlEUIe0koCzFCdHR0UFJSQl5eHq+99hr79+/n4Ycf9moZSktL0TTN7ubrSZMm0dLSQllZmcPP6u7upri42GOhHBERQVpa2oBQ7t90LcRIIqEsxAhhMBjo7u5m0qRJpKam8qc//Ylnn33Wq7Vly3SooZbY7C03NxdFUZxqwj506BDt7e0eC2Xo26+saZq1pizESCWhLMQIUVBQwKhRo6wjkS+88EK6urrcsumDvUpKSkhNTR12OpTF6NGjyczMdKqMhYWFKIpinbPrCb1DubKykvr6eqkpixFNQlmIEaKgoIDc3Fz8/f0B86pU4eHh7Ny502tlGG7Na1ucHexVWFhIWlqaR+cF5+XlUVhYSGdnJ7t27UJRFKZMmeKx5wnhKgllIUaIgoIC64IWYN70YerUqV4PZUf37500aZLdodx7gwhPDvKyyM/Px2g0UlhYyK5du8jMzCQkJMSjzxTCFRLKQowQe/bs6RPKgNdD2ZHpUBaTJ0+msLBwyB2ZTCYTd955JwkJCezduxfwTihnZGQQGhrKrl272L17tzRdixFPQlmIEaC9vZ39+/cPGsrOTjlyREdHB2VlZQ7XlCdPnmxdw9qWrq4uFi1axIsvvkhycjLz58+nrKzMK6Hs5+fHlClT2LVrl4y8FicFCWUhRoCioiJMJtOAUJ42bRrNzc02N1ZwN8t0KEdryllZWeh0OptN2O3t7Vx33XV8+OGHfPnll6xZs4a4uDjmzZtHY2Ojx0MZzE3Ymzdvpri4WEJZjHgSykKMAAUFBYwePXrAVKSJEyei0+m80oTt6HQoi8DAQLKzs22G8t///ndWr17NmjVrmDt3LmFhYXz22WfWRTq8FcrfffcdJpNJQlmMeBLKQowABQUFTJw4ccBKU4GBgUycONEroVxSUkJKSgqjRo1y+GcHG4G9e/duZs+ezYwZM6zHYmNjWblyJS+99BJRUVEuldkeliCOjIwkOTnZ488TwhUSykL02LFjh892Z7I1yMti2rRp7Nixw+NlcGbktcVgoVxUVMSECRMGHE9JSeG2225z6lmOmjx5MmCeHqUoileeKYSzJJSFAF5++WWmT5/Op59+6pPn958O1ZunR2C3trayY8cOtm7d6nB/ssXkyZMpKSkZsPrYYKHsTWFhYWRmZkrTtTgp2LVfmqqqfwTOBg4Ct+n1+q5+538JXKvX62VzUHHS2bp1K3fccQd+fn5s376dyy67zKvPP378OAcOHBgylA8fPkxdXR1jx451+Xnd3d1s2LCBDz74gI8//piSkhLAvDrXL37xC6fuOWnSJIxGIwaDwbo4R319PXV1dT4PZYDXX39dtkoUJ4Vha8qqquYDiXq9fg5QBFzb73wYIEvkiJNSTU0NV111FRdffDHXX3/9gP13vaGwsBBN06zNrP1NnToVwC1l0zSNWbNmMXfuXFatWsWNN97I559/zoEDB2hpaeG6665z6r4ZGRkEBQX1acIuLi4GGBGhfMYZZ0goi5OCPc3XZwNf9Xz9BTC73/mfA8+7s1BCeEN3dzfXXXcd4eHhvPrqq0ydOtUnoWzZQzklJcXm+YiICNLT093Sr1xZWcm2bdv48ssv2blzJ4888ggLFiwgLS3N5naG9vL392fixIl9QrmoqIjIyEhiY2NdLrcQpwt7mq+jgKqer5uAMZYTqqpGAFP0ev1jqmq75VpV1SXAEoBFixa5VNjTRXt7OwaDwdfFGNHc8Y62bt3KunXr+OSTT6iqqmLMmDHs37+f7du3Exoa6qaSDm/16tVkZWVZm5FtyczMZO3atVx55ZUO3bv/e1qzZg1+fn7ExcW5/d+xlJQUNm/ebL3vhg0bSEtLG/JzjQTy39vw5B3ZZ7D3lJ2dbfc97AnlRiC85+sIoKHXubuA54b6Yb1evwJYAWAwGDRHCne6MhgMDv0lno7c8Y5WrFhBfn4+l156KYA1iNvb25k+fbrLZbSXwWBg3rx5Q36ec845h7feesvhz9z/Pb399tvk5OR4ZNDTWWedxYoVK6zPq62tZerUqSP+32X572148o7s4473ZE971Qbggp6v5wPf9TqXCTysquoXQJaqqr9yqTRCeImmaXz44YdcccUV1mPjxo0jJibGq03YXV1dbN++nTPOOGPI66ZNm0ZRURGtra0uPW/nzp3WPmp3mzx5MqWlpdYy5w7h5wAAIABJREFUjoSR10KcbIYNZb1evxOoUVV1HTAJ+I+qqst7zt2i1+sX6PX6BUCJXq9/3LPFFcI9iouL2bdvX59QVhSlz/673rB79246OjqYNWvWkNfNnDkTk8nE9u3bXXrejh07PBrKmqZRWFhIR0cHpaWlEspCOMiuKVF6vf7+fod+auMamQ4lThofffQRCQkJA5qp8/Pz2bBhg9fKsXnzZmJiYoZd2jI+Pt7aZztnzhynntXU1ERpaanHQjk5OZmwsDD27NlDcHAw3d3dEspCOEgWDxGnpY8++ojLL798wIjj/Px8vv/+e6/sygSwZcsWzjjjDLtWmpo1axabN292+lm7d+8G8FgoK4rCpEmTKCgooKioiICAADIyMjzyLCFOVRLK4rRTV1fHhg0b+jRdW+Tn59Pa2kppaalXyrJ58+Zhm64tzjjjDLZs2eL0s3bs2EFCQoJHpyhZltssLi4mMzPTuvGEEMI+EsritPPpp58yevRozjvvvAHncnNz0el0XulXbmxspKioyO5QnjVrFmVlZVRXVzv1PE8O8rKwhLIM8hLCORLK4rTz0UcfMX/+fIKCggacCwwMJDc31yuhrNfrAfMgLntMnz4df39/p5uwvRXKFRUVbNq0SUJZCCdIKAuf8NVuTG1tbXz55Zc2m64t8vLyvBLKmzdvJisrizFjxgx/MRASEsLkyZPtbsLu/Y47OzvZs2cP06ZNc6qs9rKs320wGCSUhXCChLLwOk3TuOSSS3jkkUe8/uw33ngDk8nE5ZdfPug13poW5Uh/soW9g70qKipITU1l9erVgHl97a6uLo/XlOPi4oiOjgZGxprXQpxsJJSF133xxRd88cUXrFq1yqvPNZlMPPXUUyxevNgaHLbk5+dz6NAhGhsbPVYWTdOsI68dMWvWLLZu3Trs6PA//elPVFRU8OCDD1JVVcXOnTsJDQ31+GhoRVGsG2vk5OR49FlCnIoklIVXmUwmHnzwQcaMGcPOnTvdOvVI0zTKysro6uqyef7TTz+lqKiIe+65Z8j7WJagtEwh8oSysjJqamocrimfccYZHDt2jKKiokGvqaqqYsWKFTz77LNER0ezaNEitm/fTn5+vkubTthr8uTJxMfHExkZ6fFnCXGqkVAWXvXGG29QUFDAiy++SHNzM/v373fbvT/++GNSU1MJDg4mNzeXW2+9lYaGE0u1P/nkk1x11VVkZWUNeZ/Y2FhSUlLYuHGjy2V67733+Pvf/z7g+ObNmwkMDHR4Derc3FxCQ0OH7Fd+8skniY+P56c//SlPP/003377LStWrPB4f7LFbbfdxqOPPuqVZwlxqpFQFl7T2dnJ//7v/3L77bdz+eWXM2rUKJeXjext+/btZGVl8dZbb3HLLbewfv165s2bR1VVFZs3b2bdunX84he/sOte8+bN49tvv3W5TC+++CJLlizh008/tR5rbW1l2bJlnHnmmYwaNcqh+/n7+6Oq6qD9yjU1Nbzwwgs8+OCD1pHkTzzxBO3t7R7vT7aYPn06t99+u1eeJcSpxq5lNoVwhxUrVlBTU8Ovf/1rdDodU6ZMYceOHdxwww1uuX9hYSFTp07l6quvBuBHP/oRF110EXPmzCElJYU5c+bY3Vw8b9487r77boxGIwEBzv9nsn//fmJjY7npppvYsmULGRkZXHfddRw4cIDvvvtu+BvYMGvWLL766iub555++mmio6NZvHix9dhdd92Fv78/CxcudOp5QgjvkZqy8IqWlhYeffRR7rrrLsaNGweYa1TurCkXFhYyceJE6/fjxo3j22+/JTo6mjVr1nD//f2XcB/cvHnzaG5uZufOnU6Xp7u7m4MHD7Js2TLy8vJYuHAht956K9999x1ffvkl48ePd+q+s2bNYvfu3Rw/frzP8cbGRv7617/y4IMP9qmB+/n58fOf/3zIwW1CiJFBQll4xZ///GeMRmOf5mNLKLtjznJ3dzcGg4Hc3Nw+x8eMGcPKlSt58803rfsm22P8+PEkJCS41IRdXl5OV1cXEyZM4N1336W5uZkPPviAjz/+2KX9jM8++2y6u7vZtGlTn+PffvstHR0d/PCHP3T63kII35JQFh5XV1fHk08+yUMPPURERIT1+PTp06mvr///7d15XFXV/vDxD4OapeIsDlxTc4g0CxZaCiIolmNWmlMOWUpaZvrTnnxpt+l3w+mWpjmkXq0nr6YJiUqopCLCdVgqaIY5lI9D6HW4iqKowHn+OAcuCMgZOAP4fb9evDjttfZa66zkfM9ee+21OHPmjM11/PHHH9y+fbtQUAaoWrUqAwYMsGjmsZubm833lXMnsTVr1ox69eqxY8cOEhIS6NSpk9VlgvFZ4FatWhVqW3x8PH5+flSrVs2m8oUQziNBWdjd3/72N6pXr85bb71V4HibNm3w8PDg4MGDNteRmpqKu7s7LVq0sLmsXMHBwSQkJJCdnW3V+SdPnqR27dp5QfKxxx5DqdLZ4bSoLwzx8fEEBweXSvlCCOeQoCzs6tSpUyxcuJCPP/640FrTDz30EL6+vqVyXzk1NZUmTZoUuZ61tYKDg7l69arVzyufPHnS6vvGJQkODmb37t1kZmYCxr2Sk5OTJSgLUcZJUBZ29fHHH9OsWTOGDRtWZHppTfZKTU0tcujaFi1btqRevXpWD2H//vvvdg3Kt2/fznteedeuXRgMBgIDA+1SnxDCMSQoC7sxGAxERUXxzjvvFPtY0dNPP11qw9elHZRtva9szyvlBg0a0Lx587y2xcfH89RTT8kqWkKUcRKUhd2cPn2aa9eu4e/vX2wePz8/zp07x4ULF6yux2Aw2CUog/GKdOfOnRYvB2owGOwalKHgfWW5nyxE+SBBWdjNoUOHcHd3z9ugoCi5q0zZcrWclpZGenq63YLylStXOHLkiEXnXb58mfT0dLtuABEcHExSUhJXrlxh//79EpSFKAckKAu7SUlJoUWLFlSuXLnYPFWrVqV58+Y2BeXU1FQAuwRlX19fatWqRUJCgkXn5X8cyl6Cg4O5desWX375JdnZ2QQFBdmtLiGEY0hQFnaTkpJi1iIZ7du3Z/v27VbXk5qaSv369Qs8A11a3NzcCAgIYN++fRadd/LkSSpXrpy3epk9+Pj40KRJE+bMmUObNm1kxS4hygEJysJuzA3K/fv35+eff+b8+fNW1WOv+8m5rA3KTZs2xc3NzU6tMgoODubatWt07tzZrvUIIRxDgrKwi4yMDE6cOGFWUH7++eepXr0633//vVV1OSIop6amcuPGjUJpOTk5REZG0qlTJ7766qu84/ae5JUrNxjL/WQhygcJysIuDh8+jMFg4Mknnywxb8WKFenfvz8rV660qi5HBOWcnJxC9703btyIr68v/fv359KlS0RERJCVlQU4Lig///zzBAcHExoaave6hBD2J0G5nDp+/DjTpk1j6tSpTJ06le+++86h9R86dIiaNWvSsGFDs/IPGTKEffv2cfz4cYvquXr1KufPn7drUPb29qZRo0YFhrCzsrIYPnw4bdq04fjx42zevJm0tDRiYmIAxwXl3DW1a9SoYfe6hBD2J0G5nIqIiGDx4sX8/PPPbNy4kREjRnD69GmH1Z97P9nce6odO3akcePGZl0t5+TkcOnSJS5cuMC//vUvwD4zr/O7975y7qNIs2fPpmnTpvj4+NCjRw++/vprbt68SVpamkOCshCifJGgXA5lZ2ezceNGpk2bxu7du9m/fz8NGzZk4cKFDmuDuZO8crm7uzN48GBWrlxZ5FaO2dnZbN68mbFjx+Lj40PHjh3x9vamR48e1KlTB29v79JsfiH3BuXo6Gjatm1L48aN846Fh4fz008/sWPHDsC+j0MJIconCcrl0O7du7l48SK9e/cGwNPTk7Fjx7JkyRJu3bpVKnVkZ2fz8ccfc/bs2UJpOTk5HDp0yOI9g4cMGcKJEyeKnOk8ffp0unfvTnJyMuPHj2fVqlXs2bOHPXv2oLW2+yzngIAATp48yZUrVzAYDKxfv54+ffoUyNO9e3caNGjA1KlTcXd3LxCwhRDCHBKUy6Ho6Ghat25dYDWpN954g4yMDFatWlUqdfzwww989NFHvPfee4XSTp06xfXr1y0Oyk888QRt27Yt8v732rVrmThxIklJSbz33nv4+fnRrl072rVrx1/+8her34e5crdc1Frz22+/ceLEiUJB2cPDgzfeeIPk5GR8fHyoWLGi3dslhChfzArKSqkZSqkEpdT/VUpVyHe8t1Jqj1Jql1Jqrv2aKSwRHR1dKGDUqlWLIUOGMG/evCKHhy2Rk5PDp59+SuvWrVm1ahXJyckF0lNSUvD09MTX19fisgcPHszatWsL7GF89uxZUlJS6NWrl03ttkX16tVp3rw5+/btIzo6mgYNGuDn51co3+uvv467u7sMXQshrFJiUFZKtQUaaq2DgKNAv3zJKUBHrXUgUFeV1g7uwmrHjh3j6NGjhYIywLhx40hOTmbXrl021REZGcnRo0eJiooiMDCQKVOmFEhPSUmhVatWVKpUyeKy+/fvz/nz5wu08aeffqJatWp07NjRpnbbKve+cnR0NL1798bdvfCfT6NGjRg0aBAdOnRwQguFEGWdOVfKHYAtptexQN4no9b6tNY6y/SfdwDLttIRpW7Dhg14e3sTEBBQKK1t27Z06tSJefPmWV1+7lXykCFDeOyxx5g+fTqxsbF5k5vA+DiUOc8nF6VJkyYEBAQUWEhk06ZNdOvWjQoVKtznTPsLCAhg586dJCUlFfmlJ9d3333Hp59+6sCWCSHKi6I3uS2oBpBmen0NqHlvBqVUAFBXa11ot3ql1GhgNMDw4cOtb+kDJDMzk2PHjll17urVq+nUqRMnTpwoMr1v37689957HDhwgCpVqlhcflxcHL/88gszZszg2LFj1KlTh5CQEMaPH8/UqVOJi4tjy5YtjB071ur3EBoaytKlS3n77bfJyclh69atfPDBBwXKs6WPrFWvXj3+85//ULlyZXx8fBxevzWc0U9ljfRRyaSPzFNcP7Vo0cL8QgwGw31//P39x/r7+w8zvfb39/eff096I39//0R/f/+6JZX122+/GUTJrO2nixcvGtzd3Q0bNmwoNs/Vq1cNnp6ehnXr1llcfnZ2tuHpp582DB48uMDxw4cPG9zc3AyAwdfX1zBlyhTD9evXLS4/16lTpwyAIS4uzrBlyxYDYEhLSyuQxxn/ljIyMgweHh6GF1980eF1W0v+5komfVQy6SPz3KefSoy1uT/mXCknAROBb4HngMTcBKVUVWA1EK61/rf5XwWEpRITE3nkkUfy9h8uyvr166lUqRJdunQpNo+XlxdBQUFs2rSJl156yaI2zJ07lyNHjvDPf/6zwPHWrVsTHx+Pt7c3zZs3t6jMojRu3JhnnnmGNWvWULlyZZRSdn8O2RwPP/wwb7zxhsX9JoQQ5irxnrLWOhm4oJRKAJ4A1imlFpuS3wWaAPOVUjuUUrIqvp2MGzeOkSNHFjtzOi4ujvHjxzN8+PD77l8M0KNHD2JiYiyahZ2SksL7779PREQErVq1KpQeFBRUKgE514ABA1i3bh0bNmygR48epVaurRYtWkS3bt2c3QwhRHllyWW1rT8yBGKee/spPT3d4O7ubgAMu3btKpQ/KirKULFiRcPrr79uyMrKKrH8X3/91QAY9u/fb1Z7bt68afD19TWEhYUZsrOzzXsTNjpz5owBMACGPXv2FEqXf0vmkX4qmfRRyaSPzFMaw9eyeEgZsHfvXnJycnjyyScLzZxeu3Yt/fr1Y9y4cSxZsgQPD48Sy2vVqhWPPvoomzZtMqv+yZMnc+HCBVasWFHkY0D20KhRIwIDA6lTpw7ypJ0Q4kFhzj1lUYL09HTGjBlDRkYGYLxv+/e//53atWuXSvmJiYm0bNmSadOmMWjQIM6dO0fDhg05ceIEr732GhMnTmTGjBlmLzXp5uZGz549iYmJ4YMPPig2X1ZWFlOmTOGrr74iKiqKBg0alMr7Mdcnn3zCmTNnHPZFQAghnE0+7UpBdHQ0kZGR1KpVi1q1arFly5ZSfU41MTGRjh070rdvX+rXr8+iRYu4e/cugwcPpk2bNnz22WcWr/3co0cP9uzZw8WLF4tMP3/+PF27dmXRokWsWbOGvn37lsZbsUhISAjDhg1zeL1CCOEscqVcCqKjowkLC2PZsmUALF++nPDwcN59912aNGliU9nZ2dns3r2bzz//nAoVKjBmzBjmzJlDZmYmqampJCcn4+lp+f/GkJAQKlWqRGxsLEOHDi2QduHCBfz9/alWrRp79+61+7aIQgghjORK2Ua3b98mNja2wApPw4YNo3nz5vz1r3+1ufwjR46Qnp6et8TkqFGjSE9PZ/bs2cyfP9/qNZYrV65MaGgoMTExhdLWrl3LrVu3JCALIYSDSVC20Y4dO7h+/XqBzRI8PDz47LPPWLlyJYcOHbKp/MTERGrWrJm3IkydOnWYMGECb775ps1Duz179iQ2Npbbt28XOB4ZGUmfPn2oWrWqTeULIYSwjARlG0VHR9O+fftCi1v06dOHZ599ttBmDZZKSkqiQ4cOBSY7RUREsHDhQpv3EO7Xrx8ZGRn8+OOPeccuXbpEfHy8LJAhhBBOIEHZBgaDochtEsE4w3n69OnExMSwf/9+q+tITEy0245DdevWpW/fvnz99dd5x6Kjo6lcuTJhYWF2qVMIIUTxJCjbIDk5mbNnzxa7Y1BQUBBNmzYlNjbWqvLT0tL4448/7LplYXh4ONu2beP48eOAcei6Z8+eJa4KJoQQovRJULZBdHQ0TZs25Yknnig2T2hoKNu3b7eq/KSkJDw9Pe26eEZISAjNmjVjyZIlpKens3XrVhm6FkIIJ5GgbIPcoev73dsNCQkhMTGx0GQqcyQmJuLn58fDDz9sSzPvy93dndGjR7N8+XKioqIAXGqtaSGEeJCUyaB85coVDh48yMGDB0lOTiY7O9vhbTh79iwHDhy472b3YAzKmZmZ7N6926Lyt23bxjfffENISIgtzTTLiBEjuHbtGpMnT6Zbt24y61oIIZykzAXljIwMWrdujZ+fH35+fjz99NOMHTvW4e3YvHkzVatWJTAw8L756tevT6tWrdi2bZtZ5RoMBpYsWUJYWBg9e/YslWedS1K3bl1efPFFLl68KEPXQgjhRGUuKC9evJiMjAx+++03zp49y4oVK1i6dCmpqakObUdcXBydO3emQoUKJeYNDQ01Kyinp6fz8ssvM3fuXObPn88333xj16Hr/MaNG0f16tVLvPIXQghhP2UqKN+8eZOZM2fyzjvv0KJFCxo2bMiwYcPw8/Nj6tSpDmtHTk4OcXFxdO3a1az8oaGh7NmzJ2/DiqIcOXKEgIAA9u3bx8qVKxkzZozNzyFbIjAwkMuXL1OrVi2H1SmEEKKgMhWUlyxZQkZGBhMmTMg7lvs8cFRUlMX3bYuzfft2evfuzb///e8i0w8dOsSlS5fMfpY3ODiYu3fvkpiYWGT6unXraNeuHY0aNWL//v20bdvW6rbbQnZjEkII5yozn8KZmZnMmDGDcePGUbNmzQJpXbp0ISwsjPfffx+DwWBzXR9++CEbN24kKCiI06dPF0qPi4ujQYMGtGrVyqzyateuTdu2bYscws7KymLkyJEMHTqUzZs3U7duXZvbL4QQomwqM0F52bJlpKenM3HixCLTIyIiiI+Pt3qhjlwpKSkkJCQQFRVFlSpVCAwM5NixYwXybN26la5du1o0vFzc88rJycmkp6czadIkq3Z7EkIIUX6UiaB89+5dZsyYwZgxY6hdu3aRefz9/enbty9ffPGFTXXNmzePp556ihdeeIFt27bx6KOP0rlzZy5fvgwYr9gTEhIsXoYyJCQErTXXrl0rcDw+Pp4GDRpYvduTEEKI8sPpQTkrK4v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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#this function evaluates a model on a given validation set for n time-steps\n",
    "def eval_model(model, n, series, val_series):\n",
    "    pred_series = model.predict(n=n)\n",
    "    plt.figure(figsize=(8,5))\n",
    "    series.plot(label='actual')\n",
    "    pred_series.plot(label='forecast')\n",
    "    plt.title('MAPE: {:.2f}%'.format(mape(pred_series, val_series)))\n",
    "    plt.legend();\n",
    "    \n",
    "eval_model(my_model, 26, series_scaled, val_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, by using the best model obtained over training, according to validation loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "loading model_best_360.pth.tar\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 576x360 with 1 Axes>",
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MVlP28fHx+rQoCWUhhBBnlIaGBgICAggODh5wTkJZCCHEGefw4cN0dnZ65dnmkdeKMnCjIm9v3yihLIQQwqMqKyvJycnhrbfe8srzrU2HMvP29o0SykIIITzqN7/5Da2trVRXu2GvXhsMF8pSUxZCCHFG2LBhA2+//TajRo3yWvhZ27bRzNt9yi7ZulEIIYQYjtFo5O677+ayyy7Dz8+PxsZGr5SjoaGBMWPGWD0XGRnp1Q2BpKYshBDCI15//XV2797N888/79VmYulTFkIIccZ7/PHH+Z//+R+ysrJGdChLn7IQQojTWnt7O4cPH+biiy8GvBt+5lA2GlV26Ptu0+jtPmUJZSGEEG5XW1sH+es52JQOeC+Uu7u7aWpqIjo6mo/XwJQ7VSrrTwZzZGQk7e3ttLe3e7xsIKEshBDCA/aUNMGoGXy7KxHwXigfPXoUVVWJjo5m+WYVVYXVO0+eN29K4a1+ZQllIYQQbre1wLR618odQXR2qURFRdHa2kpXV5dHy3FyM4povt1qOrZ6Z9+aMnhvpygJZSGEEG6354APSlcVLScUVm33Xo3UPA2r4UQsFbVw1cy+NWVv76ksoSyEEMLt9JXBhHTpmDkRPlqteq1Gaq4pbykJJy4S7rlBoagcahpNtWVzKEvztRBCiNPW4cYoogIquH62wqdrYdQo74RydXU1MTExrNzmw8VaOCcX/DWwZpfpvEajITQ0VGrKQgghTk/NrSpNHdEkhtdy7Wyob4Z9R7wTypWVlSQkpvDDTrhkqkJQgMK0HPhhR99+ZQllIYQQp6Xdpab/pse3kpKgMCUbPt/gR3BwsFdCOSj+Qo63w8Va07E5+bB618lrJJSFEEKctnbuB41aR2piEADXzVb4eA1EREZ5fP3ryspK2oNmkzcORseY9lM+/2yFggNQ33SyX1n6lIUQQpyWdpao+LUXEBsbC8B1s+FIHQTGnOeVmnJt1yTmTjt57JwJ4Od7sl9ZaspCCCFOWzv3Q1eTjri4OADOSlEYEwuMmuHx8Kuo6aSmdTSXTFUsx0KCFKaedXK+soSyEEKI01KXQaXggIqhSWepKQMkRIFvYIJHw89gMFDXkY2fbzfnTex7bs4k+KFnvrKEshBCiNNScTl0dCnQttNSUwaIjQDFP9aj4VdbW4samMnYmE4CA5Q+5+ZMUthTZhopLn3KQgghTks790OQfzecKB0QykafKI+GcmVlJQRlkpmkDDiXMQZUFY7US01ZCCHEaWpniUpKzDHASExMjOV4TDh0Ee6VUJ6QHjDgXKxpIS/qmiSUhRBCnKZ27ofRo2qJjIxEo9FYjsdGKHQYwzweyj7BWWQnD4y+USGmlb1qj5pCuaWlBYPB4LGymfkNd4FWqw0HvgPGAzN0Ot3eXud8gVeBTGCbTqe7110FFUIIcWpRVZWd+2FO8qE+g7zAVFNu6wxG9WAol5U3YPSLITNp4DlFUYiLUKlrgvw4U7W5ubmZ6Ohoj5UPbKspHwcuBz60cu4KoFKn080CQrRa7TmuLJwQQohTV8txaGgG364DffqTwdRc3NYRQGvrcY9t31hcbgSwGsrmMtUePblZhqcXNgEbQlmn03XpdLq6QU6fC3zb8/VyYKarCiaEEMI19u7dy6ZNmzz+3JqeTOtoKbcaykZVAb9Ij410PlijwVfpNM2RtiIuEmqbYOzYsQAcOnTII+Xqbdjm62FEAsd6vm4GovpfoNVqFwILAebPn+/k484M7e3t6PV6bxdjRJN3ZBt5T8M73d+RqqrcfPPNhIeH88Ybbzh0D0ff0baSQCCJ2iN7SEkM7XOPlqMaIAU0MWzfvp20tDSHymaPIw1BhMc0sH9/m9XzAT5xlFX4UFVVTVRUFBs2bCA5Odnm+w/2nrKysmy+h7Oh3ASM6vk6HBhQ19fpdEuBpQB6vV61p3BnKr1eb9cf4plI3pFt5D0N73R/RytXrmTfvn1MnjzZ4c/p6DvaW6Xi56vS2VJDVlbf58ckqIAKmljCw8M98mfQ2r2DnNjOQZ+VkWxEV2wK0aysLFpbW+0qlyv+Ljk7+noDcFHP13OB9U7eTwghhAs988wz+Pj4eGUxjJqjpibhutqaAQO9IkLB18cUyp4Ygd3R0UGHMpZxid2DXhMboVDX85rGjRtHaWmp28vVn02hrNVqvwYuAV7VarULtFrtkp5TXwLJWq12LdCu0+k2uqmcQggh7LRr1y6++eYbfvKTn3gnlBtV4iOhrq5uQJ+yj49CdLiCf0iiR0K5uroagjIZn+Y/6DXmPmXwXijb1Hyt0+ku63fojZ7jBmCBa4skhBDCFZ599lmmTJnCNddcw9tvv43RaMTHx3PLU9QchehRBtrb2weEMpgGe7WHjfVIKBftrwGNlrPPah70mrhI02hxg0Fl3LhxlJWVoaoqijJwBTB3kcVDhBDiNFReXs57773Hgw8+SGRkJEajkdbWVo+WoaYRwgJOAAxovgbTXGVN8GiPhPKOItNn104IH/Qa86peDcdMNeWWlhbq6+vdXrbeJJSFEOI09PLLL5OUlMT1119vmXfr6Sbs2iYI1pjCcLCasm9gvEdCed+BLhTjcZLiBq/19qwZQu1RUygDHm/CllAWQojT0I4dO5g3bx5+fn5ERJjSxtOhXNMI/hxFURSrK2PFRoDqF+ORUC6r8iGII0M2Rfde/zo+Pp6QkBAJZSGEEM4rLy+3zLE1h7KnN1moOQo+3XVER0fj6+s74HxMOBh9PLP5Q2VjMBGBQzdFhwRBUICphq8oCunp6RLKQgghnKOqKhUVFZaVqcLCwlAUxaM15RMdKi3HwdhRbbXpGkxTkDo9tFNUw/EoEsKH7lNXFKVnqU3T770xAltCWQghTjNNTU20tbVZQtnHx4eIiAiPhrJ5ic2utsNWB3lBz+hrQ6jbQ1lVVVq7R5MSP/wa23GRUNekAhLKQgghXKCiogKgzxKRHg/lnpw93nxw0JpyTDh0GTU0NLW7tSwNzWD0GcVZVrZs7C+uV01Zmq+FEEI4rby8HEVRGDNmjOVYRESER/uUa4+CokBzfemQNWWAo63Orvg8tD37TaE/MTN42GtjI+izqld1dTVtbdbXynYHCWUhhDjNVFRUEB8fj7//ydWrvFFTjgmHhvqaIWvKAMc7g9y6faOu4BgYWsjNihn22v6regGUlZW5rWz9SSgLIcRppvcgL7PISM9tkQimPuX4SKitrR20pmwOZXevf72tuBOO72XMmMRhr+29/nVKSgq+vr4SykIIIRzXezqUmedryirxUaZ1rwcL5QB/hdCgbtC4d65ywQEffNr3WRZRGUrvPmWNRkNycrJH+5UllIUQ4jRjrabs6T7lmkYYFdhOV1cXSUlJg14XPQq3hrLBYKCoQsPEdKNNa1jHRkBTK3R2eWcEtoSyEEK40KFDh1i3bp1XyzBYKHuyplzbBAE+ps0fUlJSBr0uPsrHrc3Xz/31bQw+MTxyz5U2XR/XU5mu79m3QkJZCCFOMZ2dnTz55JNMnjyZ1NRUZs+eTUtLi1fKYjQaOXz48IDma2/0KSuGWvz9/UlISBj0urhIBb+gBLeEcmNjI4tf+ByAuTNH2/Q95lD21gIiEspCCOGkf//73yxevJjzzz+ff/7zn6iqSmVlpVfKUlNTQ1dXl9dryjVHwXD8CCkpKUNuFxkTDn5B7tkp6rHHHkMJyycl3kh4qG3bL/Ze/xpMoXzw4EEMBoPLy2eNhLIQQjipqKiIvLw8/vKXv3D99dcDeC2UzQuHWAvlY8eO0d3d7fYydBlUGo/B8aYDQzZdw8mdompra11ahr179/J///d/5J1zG/kZtkddUIBCaFDfmrLBYLC8V3eTUBZCCCfp9Xqys7MB0zrTISEhXgvl8vJyNBrNgCZj86YUzc3Nbi+DOdCa6/WkpqYOeW1MuAKaWJeH3kcffURGRgYtxlTyxtn3vbERJ+cqm3+oKC8vd2n5BiOhLIQQTtLr9WRlZQGmTQ0SExO9WlMeM2bMgCZjT+6pbF73uvbIXptqygYlwuWhXFxcTO7Es9l3EPIzbGu6Nuu9/nV4eDj+/v7U1NS4tHyDkVAWQggndHd3U1JSYgllwOuh3L/pGvDonsrmWuaRgzuHrSnHRkBHdwjlFa59X0VFRUSPPZcuA3bXlHvPVVYUhYSEBAllIYQ4FVRUVNDR0TGiQrn/yGvwbCjXNEJ4iJG2lsZha8rmVb3KK9tQVdUlz1dVFb1ej++oswkOhHHDL+TVR+/1rwHi4+MllIUQ4lSg1+sByMzMtBzzZiiXl5dbrSkHBwfj5+fnkQVEao5CREgngE01ZYD27hAaGxtd8vwjR47Q1tZGm5pObhr4+trffF0roSyEEKcevV5PYmIioaGhlmPerilbC2VFUTw2V7mmUSVE04qfnx+JiUNXU82h7MrBXsXFxQBUHYu1u+naVCbF0nwNEspCCHHK6D3y2swcyq5qjrVVZ2cn1dXVVpuvwXNzlWuOgp/ayNixY/H19R3y2rBg0PipLg/l+Ph4Cg75kT/OvloymAd6nfy9hLIQQpwieo+8NktMTKS9vd2ji3WAqdlWVVWrNWXwbCjTWTNs0zWYavCxEQrhMeNcNu2ouLiYtKxpVDXYP8gLTLX3luPQ3mH6oSo+Pp7q6mqXlG04EspCCOGEwUIZPL+AyGALh5h5alOK2qPQ0Vox7CAvs4QoCI3KcmlNOTr5fAAmOhDKcT1N6uZ+ZXNN2RMtHxLKQgjhoPb2dg4ePDiiQjkkJGTQLQo9WVNuO1pmU00ZIDUBfEPGuTSUu0OmkZoAkWH2N18nxpj+e7hnkbH4+Hg6Ojo4duyYS8o3FAllIYRwUGlpKaqqDgjl4OBgIiIiPB7K5pHXg21R6ImBXt3dKnVN0FhTaHNNOTUBuv3GuKT5+sSJExw8VM7OqkncfIFj94iLhOBAONjTYh0fHw/gkX5lCWUhhHCQXq/Hz8+PtLS0Aee8MQJ7sJHXZp6oKR+uA6MRjh8tsbmmnDZaobU7ziU15f3790P4+VQ3BfPzK+yvJYOpnzs1AQ5UmX4voSyEEKcAvV5Peno6Go1mwDlvhPLhw4eHDWV39ynrisDP1whte2yvKY+GYydCOFxZ5/SGGcXFxSij7+T8SSoZSY6FMkDaaDhQZepDjoyMRKPROBTKr3xmXz+0hLIQQjjI2iAvM2+EcnV19ZB7F3uipry1SCUl5hg+ioGkpCSbvidtNKgodPsmOj3Kefuecoi+hjuvdC7eTKFs+lpRFKvTom699VY2bNgw6D2Ky1XuftG+UPaz5SKtVvsn4FzgIHCHTqfr6jkeBCwDRgEG4BadTueZyVxCCOFler2eadOmWT2XmJjIDz/84NHy1NTUWJparfFEn/KWQkgIqaBzzBirLQjWpJiLHJhq2VDDUd/ujMPPp4PrZgc4fA8wNal/tfFkoPYP5aamJt59911+9rOfWf1+VTUFcn6Gfc8d9kcJrVabD4zR6XSzgCLghl6nLwX26nS6OcAbgPXSCSHEaWgk1ZRVVR02lCMiIjh+/DidnZ1uKYPRqLJNDyHGfTb3JwOEBiumfZVDMpzqV1ZVlYKGGeQl7CEwwPGmazDVlMtrwWA4OVe5dyibVw3rv3CM2adr4Tsd/P1e+8phS/3+XODbnq+XAzN7ndsPhPR8HQnU2/V0IYQ4RTU1NVFbWztkKFdVVWE0Gj1SnpaWFjo6OoiLixv0GndvSqGvgGNt0N282a5QBtMI7LDYXKdGYG/Yq9Luk87V0+scvkfv8nR3mwauwcAFRIqLiwkNDbW6jOjxdpV7X1L52eUwbbx9oWxL83Uk0NOyTjMQ1etcCTBeq9UWAAowoB1Hq9UuBBYCzJ8/367Cnana29sti9wL6+Qd2Ube0/AcfUe7d+8GwM/Pz+r3GwwGurq62LJlC1FRUQPOu9rBgwcB05SgwT6PeZDXjh07rI4YH4yt7+jzDWEEB8RSVbqKrNnn2fVeY0LjKQ0ex+7d/3b47+zDf4+C5n1kJnY4/fe++7gPkM6arYfpPOsEGo2GQ4cOWe67ceNGUlJSKCkpsXyP+T298GkUzS3h/OzCQ+j1xkF/cLPGllBuwtRnDBAO9N7GYz6wTqfTPa7Vam8AfvrKKeEAACAASURBVAf8pvc363S6pcBSAL1er9pTuDPVUE1iwkTekW3kPQ3P0Xe0detWQkJCOO+886zOCw4IMPVpBgUFeeTPoLbWtNLF9OnTiY6OtnpNeLhpn8TIyEi7ymTrO6r42oj2LCjYUcmUKVPsesbETCNb96TT2trq0PvasEdl7T4VDv2eiy/+cNB3YI+IUCMG3ySyshRycnL49ttvLWWrq6sjPz+/T1n1ej2hUZm8/q3Ks/9PYcYUOzuUsa35egNwUc/Xc4H1vc4pnGyyrscU2kIIcdozTz8abKEO8yhoT/Ur19TU4OfnN+hqXnAylN3VfL21CPLSOmloaLB5OpRZWqLCCWO8Q33Kqqry0BKV8aMPE+23xyWBDH2nRfVfarO4uNhqf/If3lJJjIGFVzn2zGFDWafT7QRqtFrtWmAC8JFWq13Sc/pd4AqtVvsD8CTwF8eKIYQQp5bhph8FBAQQExPj0VCOi4vDx2fw/60HBgYSGBjolrnKnV0qO/dDUPdefHx8mDp1ql3fn5oAbV1hHKqoHfbabdu2sW7dOsvvv94Ea3fDhJB3yM3Ntbvsg0kb3XdVrxMnTtDa2kp3dzclJSUDQvlIgx9Lv4DH5ito/BwbaGbTlCidTvdgv0O/6DneDMxz6MlCCHEKq6qqGjKUwbMjsGtra4cc5GXmrrnKe8qgoxNq9n/FtGnTLLVyW6WNNv23tjmIjo4OS/N/f52dndx0001ERESwbds2urtVHl6i8l8XQuEn73PZZZc5+1H6lGnTPtPXvVf18vHxoaOjY0Aov/xFJOmJcOvFjj9TFg8RQpxSVFXl5Zdf5siRI14tR3V1NaNHjx7yGk+G8nDToczcNVd5axFEh8OWte9z0UUXDf8N/fSeqzzUn+3SpUspKytjx44dNDU18da3UHgIfn1zG3v27GHmzJmDfq+90kYrlgVEzD+A1dTUWKZDZWZmWq4tqVD5ZMMonvipgp+DtWSQUBZCnGIqKytZtGgR1157Le3t7V4rhy015TFjxoy4UHZXTXlrocrE1HaKCgu5+GL7q4qBAQoJUUYITB10WlRraytPPvkkixYtQlEUPvxyG/f8VeXeG6G+YhNGo5FzzjnH2Y9ikTYaKutN+ypHRkbi5+dnCeWxY8cSEhJiufbx11XGje7kxh8590wJZSHEKWXfPlN7YmlpKXfddZdH9ri15lStKbtr/esthTBK0RMcHMyMGTMcukfaaB80YYPvq/z888/T1dXFU089Rd6kqTz6TgZnJcPiOxXWr19PTk6OS6efmZvUD9WAj48PcXFxVFdXDxjk9eUGlXdXwAPXN+Dj49yiJRLKQohTyr59+0hOTmbZsmW8+eab/P3vf/d4GY4fP86xY8dGVJ+yeaDXcFxZUzbP2W09rrLvEBw7spI5c+bg7+/v0P1SR0NgRI7VmnJdXR3PPPMMjzzyCBEREfik/5H61gje+72Cv0Zhw4YNnHvuuU59nv5Sev54e+8WZa4pm0O5sl5lwdMqv7wa5uQdd/qZEspCiFPKvn37GD9+PBdeeCHPPPMM9913H7t27fJoGcwrO9lSU66urnZ65yNb1NbWerRPee/evWRnZ/Ppp5/y0Wrw94N9m151qOnaLG00+ASlceDAgQHnnnvuOcLDw1m0aBGfr1PZXjMbtfhnxISZRkNv2rTJpf3JAMGBCvFRg4dyd7fKT55USYiCv/y3czVkMwllIcQpxRzKAPfddx+xsbGsWbPGo2WoqjL9X9qWmrLRaHR656PhnDhxgpaWFptCOTo62rLQiDPMK4gtWrSIv39s4JLJTdRWFjs0yMssNUGhQxndZ5Uss3Xr1nHTTTfR2R3IL59T+em8DtT6j1m/fj179+6lpaXF5aEMA+cql5aWUllZSXZ2Nn98BzYWwPuPKwQ5uda2mYSyEOKUoaoqBQUFllBWFIVx48ZZrVm5U3V1NRqNZtj+S/PWhYcPH3ZrecwbJdgSyuPGjaO0tNTpvviqqioiIiLo8h/P1mJfUgO+IS4uzql5wmmjob07FH1p1YBz5trp715TUVV4/u5A8vLyWL16NevXrycmJqbPaGhX6b2FY3x8PBs3bgTgm8KpPPoPlRfvVpiQ5ppABgllIcQppKamhqNHj1pCGSAtzXpzpztVVVURHx8/5EIdAHFxcWg0Gqd2PrKFPaGcmZnJsWPHqKtzbtOGyspKUlNTmXz5EmjdyRfvPspFF1006ApntkjtaXioPupPW1ub5XhjYyP19fWoIZP5+yfwwv8ohIcqzJkzh9WrV1v6k5159mD6LyDSdkLFZ8KH/O3zcF5/WGHhVa59poSyEOKUYR55nZOTYznmjVC2ZeQ1mEbsJiUleSSUFUUhJiZm2GszMkzrMe/fv9+pZ1ZWVhKbkM76klTOHr2VA2VlTvUnAyTHg6KoEJhGaWmp5bipOduHl7+byEVT4KYLTMfnzJnD1q1b+f77710+yMus91zl4z5nQf46fCLO44cXFRZc6vofAiSUhRCnjH379pGYmGjZghBOhrInp0bZMkfZbOzYsW4P5draWqKjo/HzG36RxtjYWMLCwqz229qjqqqK4yFXA7Dsb9dwxRVXcPnllzt1T3+NwpgY8AlO71M+vV6Pf8rdFB/W8Pf7FEuNePbs2RgMBiorK93SnwymmnJDM/y/vxj5/SdzoauWeQmPc06u6wMZJJSFEKeQ3oO8zNLS0jh27Jhb5t4OxtaaMngmlG2dowymfvjMzEyna8pHKivZ33YRt14MGWnxfPHFF8TGxjp1T4AJaQrBCRf2KV9xsR4l6R7++1rISDoZhjExMUyYMAGNRoNWq3X62dak9/wxf7Qanl5wBPbO4+zxzn/OwUgoCyFOGYOFMkBZWZnHymFPTTkpKckjA71sDWUwNWE7W1M+2JhMTVsCv3Bxn+rNFygcD7qYguKTc5U3FXTT4ZNstbn4kksu4dxzzyUwMNCl5TBLS1T4dLFC0dsKP70iCMDq7lCuIqEshDhlWAvlMWPGoNFoPNqvPBJryrYsHGLmbE3ZYOimMexepqTVcHaWa0P5+jmm2vyW0kTLsV1V44kLqSE3feCz/vCHP/DZZ5+5tAz9XT1LITLM1Gf/yCOPMHfuXLc9S0JZCHFKqKuro66ubkAo+/r6kpKS4rFQ7u7upqamxq4+5aqqKgwGg9vK5GhN2dF++GXfNUH4edx7TYND3z+UUSEK+UmHONBm6iPu6jJSr1zIj3IHTpMC03aU9u5I5ShFUVi8eLFNA+ocJaEshDglFBYWAgwIZfDsCOz6+nqMRqNdNWWj0ejW5TZtXc3LzDwtqr6+3u5nqarKU28FQN2HnD81YvhvcMDV57TQGXQeJYfaWPZdA2jiufXiMyOuzoxPKYQ45e3bt4+4uDiio6MHnPNkKNu6mpeZeQERdzZhO1JTBhzqV/50LRQfCYLyx+16pj1uujgSuur5v4+aefM/XdC8hlnTUt3yrJFGQlkIcUrovZJXf54MZfOSmbaGckxMDIGBgW4b7NXV1UVjY6NdARkXF0dYWJjd/crd3Sq/e01lWloJ8WGNaDQae4trk4xxKSgNy/hgTTBrCqIIO/Fln2lwpzMJZSHEKcHaIC+ztLQ0Dh48iNFodHs5qqqqiIyMJCAgwKbrFUVx6wIi5nWs7RnopSiKQyOwV+8EfQVMi19uc/O9I/z8/EjS/MDhxlF0dvswPn6f25410kgoCyFOCUOFcnp6Op2dnZamZXeyZ+S1mTtHYNuzxGZvjozAvmCKQsm7Cu1NhSQmJg7/DU6YkNJOhH8lsb7bmJDlvh8ARhoJZSHEiNfU1ER1dXWf5TV78+RcZXvmKJu5M5QdqSmDqV/ZkWlRKQkKlZWVbq0pA2RlZZLZ9RDBlQ+6dV7wSCOhLIQY8Q4dOgScDN/+oqOjCQ0N9Ui/siM1ZXc2X9fU1BAeHm734hmZmZkOT4uqqqpye005IyODQ0XfUb5/E1lZWW591kgioSyEGPHKy8tRFIUxY8ZYPa8oiscGe420mrK9C4eYZWRk0NzcTEOD/XONKysr3R7KmZmZ1NbW0t3dLaEshBAjSUVFBQkJCfj7+w96jadC2dE+5ZqaGjo7O11eHnunQ5mZ9x62d7CXefEUdzdfm6dtmffMPlNIKAshhtTY2Ehra6tXy1BRUcHYsWOHvGak15QBjhw54vLyOBrKcXFxhIaG2t2vXFtbi9FodHtNOSUlBV9fX1JTU20e6X46kFAWQgzp9ttvZ+HChV4tQ0VFBcnJyUNek56e7vZQbm1tpa2tzaGaMji3gEhZWRkdHR0DjldVVTkUyubdouytKZtXJnN3KGs0GtLS0s6opmuQUBZCDKOwsJCPPvqIxsZGr5WhvLzcppry4cOH3dJEbGbval5mERERBAcHOxXKP/rRj/jtb387oDxr1qxh1qxZDt3TlhHYBoOBfftOzhOurKxEURS3rebV26xZszjvvPPc/pyRREJZCDEog8FAeXk5nZ2dvPfee14rh63N16qqUl5ePuR1zjCv5mVvTVlRFKcGe7W2tlJeXs6SJUtoamqyHF+yZAmxsbFcf/31Dt3Xlpryu+++y/XXX28pe1VVFXFxcfj5+Tn0THv885//5NFHH3X7c0YSCWUhxKAOHz6MwWBg6tSpvPHGG14pQ3d3N0eOHBk2lFNTUwHXzFU+dOgQ27ZtG3C8qqoKf39/h5Z8HDt2rMNLbZqD02AwsGTJEgA6Ozt55ZVXuOuuuxxe7jI9PX3Y9/Wf//wHo9Fo+aHMEyOvz2QSykKIQZn7aP/3f/+XrVu3UlBQ4PEy1NTU0NXVNWyfcmhoKLGxsS7pV3766aeZPXs2e/bs6XN848aNJCYmoij27yHsTE25pKQEf39/fvWrX/HCCy/Q0dHBBx98wNGjR53q709PT6exsZHm5mar57u7u/nuu++Iiori7bffBvDIwiFnMgllIcSgysrKiIyMZO7cuWRnZ3ultmwOsuFqyuC6EdiHDh3ixIkTXHPNNZa+9CVLlvDCCy/wxBNPOHRPZxYQKSkpYdy4cdx99900NTXxzjvv8NJLL3HTTTc51bdrXoxlsHe2fft2GhoaeOSRR9i9ezd79+71yMIhZzKbQlmr1f5Jq9Wu1Wq1b2m1Wk2/c/+l1WpXabXaH7Ra7TnuKaYQwhsOHDhAeno6iqKwYMEC3nrrLbq6ujxahoqKCjQajU3h46oR2OXl5dx///2oqsqPf/xjli1bxl133cWzzz7L7bff7tA9nakp6/V6srKyiIuLY/78+Tz00ENs3ryZu+++26H7mSUlJeHn5zfoO/vmm29IS0vjiiuuICMjg3feeUdqym42bChrtdp8YIxOp5sFFAE39DqXCFwNXKjT6c7X6XQb3VZSIYTHlZWVWWpTt912G3V1dXzzzTceLUN5eTlJSUn4+Axfh3BFTdk8WCw/P59PP/2UdevWcfPNN/Pggw/yq1/9yuH7jh07lvr6ek6cOGH395aUlFgW+/jVr35FfX0906dPZ+rUqQ6XB0y7MSUnJw/ar7x8+XLmzZuHoijceuutvPPOOxw5ckRqym5kS035XODbnq+XAzN7nZsHdADf9dSiQ11cPiGEF5lrygBjxozhoosu4v333/doGWwZeW3milBuamqitbWV5ORk8vLy+OCDD3jiiSf44x//6NR9zX3ijtSWe4dyZmYmTz/9tNPlMRtssFdzczObNm1i7ty5ANx6661UVFRQU1MjoexGtoRyJHCs5+tmIKrXuXggBrgY2Aj8t0tLJ4Twqt41ZYCZM2eyfft2j5bB3lCur6+npaXF4eeZp1SZQ/Syyy7jsccec2hwV2/mbgC9Xm/X9x09epT6+vo+i2j85je/4fzzz3eqPGaD/SCzcuVKFEXhRz/6EWD6YWDatGmA/VPChO1smWjWBIzq+TocaOx37nudTqdqtdqVwIAJZVqtdiGwEGD+/PnOlfYM0d7ebvc/3DONvCPbOPOejh8/Tm1tLf7+/pZ7xMTEUFxczJ49ezy29GFJSQkzZsyw63N8//33nHXWWTZd2/8dbdy4EUVRaGtrc/nfsTFjxrBu3Tq7VqnavXs3AL6+vm75Oz9q1CiKiooG3Pv9999n8uTJVFdXW97RxRdfzJYtWzhx4oT8+7NisH9v9vx52xLKG4D7gTeBucD6XufWAw/2fD0JGNAGotPplgJLAfR6vXqmLZnmCPOgDjE4eUe2ceY97d27FzCtqmRuOvX392fRokV0dnYyceJEl5VzKLW1tUyaNMmmz5GWloaPjw+qqtr8ufu/oxUrVjB69Ghyc3MdLvNgcnNzaWxsHLRsO3fuZPHixTz11FOWPYS3bt1KcHAw5513ntO1dWumTp3K3/72NzIyMiz99qqqsmnTJn75y1+SlZVleUe/+c1viIuLY9asWW4py6nOFf9fGrb5WqfT7QRqtFrtWmAC8JFWq13Sc243UKHVan8A7gBecqo0QogR48CBAyiKQkpKiuVYSkoK4eHh7Nq1yyNl6OzspKamxubma41Gw9ixY53qVy4vLx92TrSjsrOzKS4uHnC8tbWVBx54AK1Wy8cff8y//vUvyzm9Xk9GRobbQjA9PZ2Ojg7LEqIAxcXFlJeXW/qTzcLCwrj77rslkN3IpnXSdDrdg/0O/aLXuUdcWiIhxIhQVlZGUlJSn+0SFUUhLy/P0qTqbkeOHEFVVZtDGZwf7GXLOtuOys7OHrBcaUdHB5MnT+bo0aO8/vrr7N69m6+++oo//OEPgKn53p2tQr3nKpv3q16xYgUxMTFMmjTJbc8V1sniIUIIq3qPvO4tPz/fYzXl/oOubOGKUHZnTbmmpqbPClq7du2ipKSEDRs2cNttt3H55Zeze/duy5KcvUdeu0N0dDRhYWF9RmCvW7eOWbNm2TQNTbiWvHEhhFX9R16bmUNZVVW3l6GiooKQkBC71poe6aEM9GnC3rp1K7GxsWRkZACmEe6jRo3i66+/RlVV9Hq9W0NZUZQ+70xVVdauXevwzlPCORLKQgirhqopHz161OHNFexhng5lTx+mOWAc+aHBYDBw5MgRt4VyYmIioaGhA0J56tSpls+o0Wi45JJL+Prrr6mrq+PYsWNuH9SYlpZmqSkfOHCAyspKCWUvkVAWQgygquqgNeUJEybg4+PjkSbsiooKuwMyLS2NtrY26uvr7X5eZWUlRqPRbaGsKApZWVlWQ7m3yy+/nBUrVlhGwLuzpgx9lyddu3YtISEh0p/sJRLKQogB6urqOH78uNWacnBwMJmZmR4JZUcGXZnL7MgWjubVttwVymBqwi4qKgKgpaWFwsLCAaE8b9482tra+Mc//sGoUaOIjY11W3mgb0157dq1nHPOOR7ZL1kMJKEshBjA/D9oazVl8NxgL3tW8zJLSEggMDDQoX7l8vJygoKCiI6Otvt7bdV7WtT27dtRVXVAKCckJKDVavnggw/Iyspy+xSk9PR0KisraW9vtwzyEt4hoSyEGODAgQMEBgaSkJBg9fxIDmVFUUhNTXU4lO3tw7ZXdnY2JSUldHd3s3XrVpKTk4mLixtw3eWXX47BYHB70zWYfvhSVRWdTkdxcbGEshdJKAshBjD3Jw8WTvn5+ZSUlNDW1ua2MrS2tnL06FGHmpIdHYHtzpHXZtnZ2XR0dFBeXm61P9nssssuA9zfnwyQmpoKwJtvvomfnx/Tp093+zOFdRLKQogBBht5bZafn4+qqhQUFDj9rMOHD3PllVeyZs0ay7GWlhYWLFiARqMhJyfH7nuO5FA2j6QuLi5Gp9MNGsparZbc3FzOOcf929QHBweTkJDAsmXLmDJlCsHBwW5/prBOQlkIMcBgI6/NxowZQ1RUlEuasFetWsWXX37JnDlzuOOOO1i3bh1Tp05l48aNrF692rLKlD1sDeVHH32UN9980/J7T4RySEgISUlJbNy4kbKyskFD2cfHhz179jBv3jy3lscsPT2d5uZmabr2MgllIcQA+/fvtyxmYY2iKC7rVy4sLESr1fLFF1+wcuVKZs2axejRo9m+fbvDtcT09HTKy8vp7u4e9JoPPviAxYsX8/zzz9PU1AQ4NgXLEdnZ2bzzzjsATJkyxe3Ps4X5hzAJZe+SUBZC9HHixAkqKiqGDGXAZWtgFxYWkpOTwxVXXMG+ffv45JNP+O6774iPj3f4nmlpaXR1dXHkyBGr5ysqKli4cCG/+MUv8Pf3Z8mSJbS0tDjch22v7OxsSktLyc7OJjw83O3Ps4W5u2LmzJleLsmZTUJZCNGHeTrUcAOMcnNzKSgocHq5TXMog6lp95prrnF6jqy51mdtrnJ3dze33347ycnJvPDCC9xyyy28+OKL7N+/H3DvHGUz817PgzVde8PcuXO588473TodTAxPQlkI0cf+/fvx8fGxjMgdjHlv4Orqaoef1dHRQWlpqUODuYYSERFBRESE1X7l559/nk2bNvHuu+8SGBjIT37yE44ePcrTTz8NQFJSkkvLYo15DWytVuv2Z9lq5syZLF261NvFOONJKAsh+ti/fz+pqal9tmy0Zvz48QCWpSAdYZ6v6+pQBtMoZ/PKWb3961//4p577mHChAmAaZekBQsW8MEHHxAbG0tQUJDLy9LfhAkT8PX1laZiMYCEshAjSGFhIYsXL/bIDkyDKSkpGbY/GWDUqFEkJyc7FcqFhYVoNBrGjRvn8D0Gk5eXN2AgWkdHB0VFRQPm4d5///0oiuKRpmswjV4/dOjQiKopi5FBQlmIEeT999/n0Ucf9Woz4v79+21esMLcr+yowsJCsrKy3LLOsrXR4YWFhRgMBvLz8/scz8zM5Oabb7bU/j3Bkale4vQnoSzECFJQUEBoaCj33Xef1aZXT7C1pgymUHa2puyOpmswhXJ1dTW1tbWWY7t27SIsLMxqf/mbb77Ja6+95payCGErCWUhRpC9e/fywAMPMGXKFG655RY6Ojo8+vz29nabpkOZmWvKRqPRoee5M5Tz8vIA+tSWd+3aRV5eHj4+A//Xp9Fo0Gg0bimLELaSUBZihOjo6KCkpIS8vDzefvttSktLefTRRz1ahrKyMlRVtbn5esKECbS2tlJeXm73s7q7uykuLnZbKIeHh5OamjoglPs3XQsxkkgoCzFC6PV6uru7mTBhAikpKfz5z3/mxRdf9Ght2TwdaqglNnvLyclBURSHmrAPHTpEe3u720IZ+vYrq6pqqSkLMVJJKAsxQhQUFBAQEGAZiXzxxRfT1dXlkk0fbFVSUkJKSsqw06HMgoKCyMjIcKiMhYWFKIpimbPrDr1DubKykoaGBqkpixFNQlmIEaKgoICcnBx8fX0B06pUo0aNYufOnR4rw3BrXlvj6GCvwsJCUlNT3TovOC8vj8LCQjo7O9m1axeKojBx4kS3PU8IZ0koCzFCFBQUWBa0ANOmD5MmTfJ4KNu7f++ECRNsDuXeG0S4c5CXWX5+PgaDgcLCQnbt2kVGRgYhISFufaYQzpBQFmKE2Lt3b59QBjweyvZMhzLLzc2lsLBwyB2ZjEYjd999N4mJiezbtw/wTCinp6cTGhrKrl272L17tzRdixFPQlmIEaC9vZ3S0tJBQ9nRKUf26OjooLy83O6acm5urmUNa2u6urqYP38+r776KmPHjmXu3LmUl5d7JJR9fHyYOHEiu3btkpHX4pQgoSzECFBUVITRaBwQymeffTYtLS1WN1ZwNfN0KHtrypmZmWg0GqtN2O3t7dx444189tlnfPPNN3z//ffEx8czZ84cmpqa3B7KYGrC3rx5M8XFxRLKYsSTUBZiBCgoKCAoKGjAVKTx48ej0Wg80oRt73QoM39/f7KysqyG8j/+8Q9WrVrF999/z+zZswkLC+Prr7+2LNLhqVBev349RqNRQlmMeBLKQowABQUFjB8/fsBKU/7+/owfP94joVxSUkJycjIBAQF2f+9gI7B3797NzJkzmTJliuVYXFwcK1as4LXXXiMyMtKpMtvCHMQRERGMHTvW7c8TwhkSykL02LFjh9d2Z7I2yMvs7LPPZseOHW4vgyMjr80GC+WioiLOOuusAceTk5O54447HHqWvXJzcwHT9ChFUTzyTCEcJaEsBPD6668zefJkvvrqK688v/90qN7cPQK7ra2NHTt2sHXrVrv7k81yc3MpKSkZsPrYYKHsSWFhYWRkZEjTtTgl2LRfmlar/RNwLnAQuEOn03X1O/8QcINOp5PNQcUpZ+vWrdx11134+Piwfft2rrjiCo8+//jx4xw4cGDIUD5y5Ah1dXXExsY6/bzu7m42bNjAp59+yhdffEFJSQlgWp3r17/+tUP3nDBhAgaDAb1eb1mco6Ghgbq6Oq+HMsA777wjWyWKU8KwNWWtVpsPjNHpdLOAIuCGfufDAFkiR5ySampquPbaa7n00ku56aabBuy/6wmFhYWoqmppZu1v0qRJAC4pm6qqTJ8+ndmzZ7Ny5Up+/OMf85///IcDBw7Q2trKjTfe6NB909PTCQwM7NOEXVxcDDAiQnnatGkSyuKUYEvz9bnAtz1fLwdm9jt/D/A3VxZKCE/o7u7mxhtvZNSoUbz55ptMmjTJK6Fs3kM5OTnZ6vnw8HDS0tJc0q9cWVnJtm3b+Oabb9i5cydPPPEE8+bNIzU11ep2hrby9fVl/PjxfUK5qKiIiIgI4uLinC63EGcKW5qvI4Gqnq+bgSjzCa1WGw5M1Ol0T2m11luutVrtQmAhwPz5850q7Jmivb0dvV7v7WKMaK54R1u3bmXt2rV8+eWXVFVVERUVRWlpKdu3byc0NNRFJR3eqlWryMzMtDQjW5ORkcGaNWu4+uqr7bp3//f0/fff4+PjQ3x8vMv/jiUnJ7N582bLfTds2EBqauqQn2skkH9vw5N3ZJvB3lNWVpbN97AllJuAUT1fhwONvc7dC7w01DfrdLqlwFIAvV6v2lO4M5Ver7frD/FM5Ip3J+xZfQAAIABJREFUtHTpUvLz87n88ssBLEHc3t7O5MmTnS6jrfR6PXPmzBny85x33nm8//77dn/m/u9p2bJlZGdnu2XQ0znnnMPSpUstz6utrWXSpEkj/u+y/Hsbnrwj27jiPdnSXrUBuKjn67nA+l7nMoBHtVrtciBTq9X+1qnSCOEhqqry2WefcdVVV1mOjR49mpiYGI82YXd1dbF9+3amTZs25HVnn302RUVFtLW1OfW8nTt3WvqoXS03N5eysjJLGUfCyGshTjXDhrJOp9sJ1Gi12rXABOAjrVa7pOfcbTqdbp5Op5sHlOh0usXuLa4QrlFcXMz+/fv7hLKiKH323/WE3bt309HRwfTp04e8burUqRiNRrZv3+7U83bs2OHWUFZVlcLCQjo6OigrK5NQFsJONk2J0ul0D/Y79Asr18h0KHHK+Pzzz0lMTBzQTJ2fn8+GDRs8Vo7NmzcTExMz7NKWCQkJlj7bWbNmOfSs5uZmysrK3BbKY8eOJSwsjL179xIcHEx3d7eEshB2ksVDxBnp888/58orrxww4jg/P589e/Z4ZFcmgC1btjBt2jSbVpqaPn06mzdvdvhZu3fvBnBbKCuKwoQJEygoKKCoqAg/Pz/S09Pd8iwhTlcSyuKMU1dXx4YNG/o0XZvl5+fT1tZGWVmZR8qyefPmYZuuzaZNm8aWLVscftaOHTtITEx06xQl83KbxcXFZGRkWDaeEELYRkJZnHG++uorgoKCuOCCCwacy8nJQaPReKRfuampiaKiIptDefr06ZSXl1NdXe3Q89w5yMvMHMoyyEsIx0goizPO559/zty5cwkMDBxwzt/fn5ycHI+Esk6nA0yDuGwxefJkfH19HW7C9lQoHz58mE2bNkkoC+EACWXhFd7ajenEiRN88803VpuuzfLy8jwSyps3byYzM5OoqKjhLwZCQkLIzc21uQm79zvu7Oxk7969nH322Q6V1Vbm9bv1er2EshAOkFAWHqeqKpdddhlPPPGEx5/973//G6PRyJVXXjnoNZ6aFmVPf7KZrYO9Dh8+TEpKCqtWrQJM62t3dXW5vaYcHx9PdHQ0MDLWvBbiVCOhLDxu+fLlLF++nJUrV3r0uUajkWeffZYFCxZYgsOa/Px8Dh06RFNTk9vKoqqqZeS1PaZPn87WrVuHHR3+5z//mcOHD/Pwww9TVVXFzp07CQ0NdftoaEVRLBtrZGdnu/VZQpyOJJSFRxmNRh5++GGioqLYuXOnS6ceqapKeXk5XV1dVs9/9dVXFBUVcf/99w95H/MSlOYpRO5QXl5OTU2N3TXladOmcezYMYqKiga9pqqqiqVLl/Liiy8SHR3N/Pnz2b59O/n5+U5tOmGr3NxcEhISiIiIcPuzhDjdSCgLj/r3v/9NQUEBr776Ki0tLZSWlrrs3l988QUpKSkEBweTk5PD7bffTmPjyaXan3nmGa699loyMzOHvE9cXBzJycls3LjR6TJ9/PHH/OMf/xhwfPPmzfj7+9u9BnVOTg6hoaFD9is/88wzJCQk8Itf/ILnnnuO1atXs3TpUrf3J5vdcccdPPnkkx55lhCnGwll4TGdnZ387ne/4+c//zlXXnklAQEBTi8b2dv27dvJzMzk/fff57bbbmPdunXMmTOHqqoqNm/ezNq1a/n1r39t073mzJnD6tWrnS7Tq6++ysKFC/nqq68sx9ra2nj++eeZMWMGAQEBdt3P19cXrVY7aL9yTU0Nr7zyCg8//LBlJPnTTz9Ne3u72/uTzSZPnszPf/5zjzxLiNONTctsCuEKS5cupaamhsceewyNRsPEiRPZsWMHN998s0vuX1hYyKRJk7juuusA+OlPf8oll1zCrFmzSE5OZtasWTY3F8+ZM4f77rsPg8GAn5/j/0xKS0uJi4vjlltuYcuWLaSnp3PjjTdy4MAB1q9fP/wNrJg+fTrffvut1XPPPfcc0dHRLFiwwHLs3nvvxdfXl2uuucah5wkhPEdqysIjWltb+f/t3Xtc1UX++PEXFzVLRcULomypqUReCoYsBQkUy0tGpWneuyhpmeVX+uVq28XvRqZrmuYlbbP95epqQqISKqmEsF5GBcwo1PLnZdH1soqiqMD5/XEOLAjIuXAOB3w/Hw8fHD8zn5k5o5z3+cxnPjMzZ87kzTffpFWrVoDxiqoqr5QzMzPx8/Mr/nurVq1ISkrC09OT7du3ExV16xLuFQsJCeHy5cukpaVZ3Z6CggKOHTvGp59+SteuXYmIiGD06NGkpKSwefNm2rdvb1W53bt3JyMjg6tXr5Y6fvHiRT7//HOmTZtW6grc1dWVyZMn33ZymxDCOUhQFg4xd+5c8vPzSw0fFwXlqnhmuaCggKysLB544IFSx5s2bUpiYiKrV68u3jfZHO3bt8fb29umIewTJ05w8+ZNfH19+fbbb7l8+TLfffcdGzZssGk/4x49elBQUMCuXbtKHU9KSuL69euMHDnS6rKFENVLgrKwu7NnzzJ79mz++Mc/4uHhUXzc39+f8+fPc+LECZvr+P3337l+/XqZoAzQsGFDhg4datHMYxcXF5vvKxdNYmvfvj0tW7Zkx44dJCcn06tXL6vLBOOzwL6+vmXalpSUhL+/P40aNbKpfCFE9ZGgLOzuz3/+M40bN+a1114rdbxLly64ublx4MABm+vIzMzE1dWVjh072lxWkZCQEJKTkykoKLDq/KNHj9KsWbPiIHn//fejVNXscFreF4akpCRCQkKqpHwhRPWQoCzs6tixYyxevJgPPvigzFrTd911F35+flVyXzkzM5O2bduWu561tUJCQrh48aLVzysfPXrU6vvGlQkJCWHXrl3k5eUBxr2S09LSJCgLUcNJUBZ29cEHH9C+fXtGjx5dbnpVTfbKzMwsd+jaFp06daJly5ZWD2H/9ttvdg3K169fL35eeefOnRgMBoKCguxSnxDCMSQoC7sxGAzExsbyxhtvVPhY0cMPP1xlw9dVHZRtva9szytlb29vOnToUNy2pKQkHnroIVlFS4gaToKysJvjx49z6dIlAgICKszj7+/PqVOnOHPmjNX1GAwGuwRlMF6R/vjjjxYvB2owGOwalKH0fWW5nyxE7SBBWdhNRkYGrq6uxRsUlKdolSlbrpazs7PJycmxW1C+cOEChw4dsui88+fPk5OTY9cNIEJCQkhNTeXChQvs27dPgrIQtYAEZWE36enpdOzYkfr161eYp2HDhnTo0MGmoJyZmQlgl6Ds5+eHp6cnycnJFp1X8nEoewkJCeHatWt89tlnFBQUEBwcbLe6hBCOIUFZ2E16erpZi2R0796d7du3W11PZmYmrVq1KvUMdFVxcXEhMDCQvXv3WnTe0aNHqV+/fvHqZfbg4+ND27ZtmTdvHl26dJEVu4SoBSQoC7sxNygPGTKEH374gdOnT1tVj73uJxexNii3a9cOFxcXO7XKKCQkhEuXLvH444/btR4hhGNIUBZ2kZuby5EjR8wKyk8++SSNGzfmH//4h1V1OSIoZ2ZmcuXKlTJphYWFxMTE0KtXLz7//PPi4/ae5FWkKBjL/WQhagcJysIuDh48iMFgoGvXrpXmrVu3LkOGDGHlypVW1eWIoFxYWFjmvvfGjRvx8/NjyJAhnDt3jujoaPLz8wHHBeUnn3ySkJAQwsLC7F6XEML+JCjXUocPH2bGjBlMnz6d6dOn88033zi0/oyMDJo2bUrr1q3Nyj9ixAj27t3L4cOHLarn4sWLnD592q5B2cvLizZt2pQaws7Pz2fMmDF06dKFw4cPs3nzZrKzs4mPjwccF5SL1tRu0qSJ3esSQtifBOVaKjo6mqVLl/LDDz+wceNGxo4dy/Hjxx1Wf9H9ZHPvqfbs2ZN7773XrKvlwsJCzp07x5kzZ/jnP/8J2GfmdUm33lcuehRpzpw5tGvXDh8fH/r3788XX3zB1atXyc7OdkhQFkLULhKUa6GCggI2btzIjBkz2LVrF/v27aN169YsXrzYYW0wd5JXEVdXV4YPH87KlSvL3cqxoKCAzZs3M3HiRHx8fOjZsydeXl7079+f5s2b4+XlVZXNL+PWoBwXF0e3bt249957i49FRkby/fffs2PHDsC+j0MJIWonCcq10K5duzh79ixPPfUUAO7u7kycOJFly5Zx7dq1KqmjoKCADz74gJMnT5ZJKywsJCMjw+I9g0eMGMGRI0fKnen88ccf069fP9LS0pg8eTKrVq1i9+7d7N69G6213Wc5BwYGcvToUS5cuIDBYGD9+vUMGjSoVJ5+/frh7e3N9OnTcXV1LRWwhRDCHBKUa6G4uDg6d+5cajWpV155hdzcXFatWlUldXz77be8//77vP3222XSjh07xuXLly0Oyg8++CDdunUr9/732rVrmTJlCqmpqbz99tv4+/vzyCOP8Mgjj/CHP/zB6vdhrqItF7XW/Prrrxw5cqRMUHZzc+OVV14hLS0NHx8f6tata/d2CSFqF7OCslJqllIqWSn1f5VSdUocf0optVsptVMpNd9+zRSWiIuLKxMwPD09GTFiBAsWLCh3eNgShYWFzJw5k86dO7Nq1SrS0tJKpaenp+Pu7o6fn5/FZQ8fPpy1a9eW2sP45MmTpKenM3DgQJvabYvGjRvToUMH9u7dS1xcHN7e3vj7+5fJ9/LLL+Pq6ipD10IIq1QalJVS3YDWWutg4BdgcInkdKCn1joIaKGqagd3YbWsrCx++eWXMkEZYNKkSaSlpbFz506b6oiJieGXX34hNjaWoKAgpk2bVio9PT0dX19f6tWrZ3HZQ4YM4fTp06Xa+P3339OoUSN69uxpU7ttVXRfOS4ujqeeegpX17K/Pm3atOGFF16gR48e1dBCIURNZ86Vcg9gi+l1AlD8yai1Pq61zjf99QZg2VY6ospt2LABLy8vAgMDy6R169aNXr16sWDBAqvLL7pKHjFiBPfffz8ff/wxCQkJxZObwPg4lDnPJ5enbdu2BAYGllpIZNOmTfTt25c6derc5kz7CwwM5McffyQ1NbXcLz1FvvnmG2bOnOnAlgkhaovyN7ktrQmQbXp9CWh6awalVCDQQmtdZrd6pdR4YDzAmDFjrG/pHSQvL4+srCyrzl29ejW9evXiyJEj5aZHRETw9ttvs3//fho0aGBx+YmJifz000/MmjWLrKwsmjdvTmhoKJMnT2b69OkkJiayZcsWJk6caPV7CAsLY/ny5bz++usUFhaydetW3n333VLl2dJH1mrZsiX/+c9/qF+/Pj4+Pg6v3xrV0U81jfRR5aSPzFNRP3Xs2NH8QgwGw23/BAQETAwICBhteh0QEBCw8Jb0NgEBASkBAQEtKivr119/NYjKWdtPZ8+eNbi6uho2bNhQYZ6LFy8a3N3dDevWrbO4/IKCAsPDDz9sGD58eKnjBw8eNLi4uBgAg5+fn2HatGmGy5cvW1x+kWPHjhkAQ2JiomHLli0GwJCdnV0qT3X8X8rNzTW4ubkZnnnmGYfXbS35nauc9FHlpI/Mc5t+qjTWFv0x50o5FZgC/A14AkgpSlBKNQRWA5Fa63+b/1VAWColJYV77rmneP/h8qxfv5569erRu3fvCvN4eHgQHBzMpk2bePbZZy1qw/z58zl06BB///vfSx3v3LkzSUlJeHl50aFDB4vKLM+9997Lo48+ypo1a6hfvz5KKbs/h2yOu+++m1deecXifhNCCHNVek9Za50GnFFKJQMPAuuUUktNyW8CbYGFSqkdSilZFd9OJk2axEsvvVThzOnExEQmT57MmDFjbrt/MUD//v2Jj4+3aBZ2eno677zzDtHR0fj6+pZJDw4OrpKAXGTo0KGsW7eODRs20L9//yor11ZLliyhb9++1d0MIURtZcllta1/ZAjEPLf2U05OjsHV1dUAGHbu3Fkmf2xsrKFu3bqGl19+2ZCfn19p+T///LMBMOzbt8+s9ly9etXg5+dnCA8PNxQUFJj3Jmx04sQJA2AADLt37y6TLv+XzCP9VDnpo8pJH5mnKoavZfGQGmDPnj0UFhbStWvXMjOn165dy+DBg5k0aRLLli3Dzc2t0vJ8fX2577772LRpk1n1R0VFcebMGVasWFHuY0D20KZNG4KCgmjevDnypJ0Q4k5hzj1lUYmcnBwmTJhAbm4uYLxv+5e//IVmzZpVSfkpKSl06tSJGTNm8MILL3Dq1Clat27NkSNHePHFF5kyZQqzZs0ye6lJFxcXBgwYQHx8PO+++26F+fLz85k2bRqff/45sbGxeHt7V8n7MdeHH37IiRMnHPZFQAghqpt82lWBuLg4YmJi8PT0xNPTky1btlTpc6opKSn07NmTiIgIWrVqxZIlS7h58ybDhw+nS5cufPTRRxav/dy/f392797N2bNny00/ffo0ffr0YcmSJaxZs4aIiIiqeCsWCQ0NZfTo0Q6vVwghqotcKVeBuLg4wsPD+fLLLwH46quviIyM5M0336Rt27Y2lV1QUMCuXbuYO3cuderUYcKECcybN4+8vDwyMzNJS0vD3d3yf8bQ0FDq1atHQkICo0aNKpV25swZAgICaNSoEXv27LH7tohCCCGM5ErZRtevXychIaHUCk+jR4+mQ4cO/OlPf7K5/EOHDpGTk1O8xOS4cePIyclhzpw5LFy40Oo1luvXr09YWBjx8fFl0tauXcu1a9ckIAshhINJULbRjh07uHz5cqnNEtzc3Pjoo49YuXIlGRkZNpWfkpJC06ZNi1eEad68OW+99RavvvqqzUO7AwYMICEhgevXr5c6HhMTw6BBg2jYsKFN5QshhLCMBGUbxcXF0b179zKLWwwaNIjHHnuszGYNlkpNTaVHjx6lJjtFR0ezePFim/cQHjx4MLm5uXz33XfFx86dO0dSUpIskCGEENVAgrINDAZDudskgnGG88cff0x8fDz79u2zuo6UlBS77TjUokULIiIi+OKLL4qPxcXFUb9+fcLDw+1SpxBCiIpJULZBWloaJ0+erHDHoODgYNq1a0dCQoJV5WdnZ/P777/bdcvCyMhItm3bxuHDhwHj0PWAAQMqXRVMCCFE1ZOgbIO4uDjatWvHgw8+WGGesLAwtm/fblX5qampuLu723XxjNDQUNq3b8+yZcvIyclh69atMnQthBDVRIKyDYqGrm93bzc0NJSUlJQyk6nMkZKSgr+/P3fffbctzbwtV1dXxo8fz1dffUVsbCyAU601LYQQd5IaGZQvXLjAgQMHOHDgAGlpaRQUFDi8DSdPnmT//v233ewejEE5Ly+PXbt2WVT+tm3b+PrrrwkNDbWlmWYZO3Ysly5dIioqir59+8qsayGEqCY1Lijn5ubSuXNn/P398ff35+GHH2bixIkOb8fmzZtp2LAhQUFBt83XqlUrfH192bZtm1nlGgwGli1bRnh4OAMGDKiSZ50r06JFC5555hnOnj0rQ9dCCFGNalxQXrp0Kbm5ufz666+cPHmSFStWsHz5cjIzMx3ajsTERB5//HHq1KlTad6wsDCzgnJOTg7PPfcc8+fPZ+HChXz99dd2HbouadKkSTRu3LjSK38hhBD2U6OC8tWrV/nkk09444036NixI61bt2b06NH4+/szffp0h7WjsLCQxMRE+vTpY1b+sLAwdu/eXbxhRXkOHTpEYGAge/fuZeXKlUyYMMHm55AtERQUxPnz5/H09HRYnUIIIUqrUUF52bJl5Obm8tZbbxUfK3oeODY21uL7thXZvn07Tz31FP/+97/LTc/IyODcuXNmP8sbEhLCzZs3SUlJKTd93bp1PPLII7Rp04Z9+/bRrVs3q9tuC9mNSQghqleN+RTOy8tj1qxZTJo0iaZNm5ZK6927N+Hh4bzzzjsYDAab63rvvffYuHEjwcHBHD9+vEx6YmIi3t7e+Pr6mlVes2bN6NatW7lD2Pn5+bz00kuMGjWKzZs306JFC5vbL4QQomaqMUH5yy+/JCcnhylTppSbHh0dTVJSktULdRRJT08nOTmZ2NhYGjRoQFBQEFlZWaXybN26lT59+lg0vFzR88ppaWnk5OQwdepUq3Z7EkIIUXvUiKB88+ZNZs2axYQJE2jWrFm5eQICAoiIiODTTz+1qa4FCxbw0EMP8fTTT7Nt2zbuu+8+Hn/8cc6fPw8Yr9iTk5MtXoYyNDQUrTWXLl0qdTwpKQlvb2+rd3sSQghRe1R7UM7Pz2fOnDns37+/wjyrV6/mzJkzFV4lFxk3bhyJiYmcOHHCqracP3+elStX8sYbb+Di4oKHhwfx8fHUqVOHqVOnAsZVtq5du0bv3r0tKrtXr164uLiUGcJOSkoiJCTEoZO6hBBCOKdqD8rffvstUVFRBAQE0Ldv3zJBy2AwMHv2bEaNGkWrVq1uW1bfvn3x8vLib3/7m1VtWb58Offccw/Dhg0rPtagQQOWLFnCihUrSExMJDExkc6dO1fallt5eHgQGhrKunXrio8VFBSQnJxMSEiIVe0VQghRu1RrUC4ZcHfs2IG7uzu9e/dm3rx5xXk2b97MwYMHi69Ub8fd3Z1Ro0axYsUKiyd85efns2jRIsaPH19mM4Z+/foxYsQIxo8fz8aNG81+FOpWzz//POvXr+fatWuAcRb3xYsXJSgLIYQAqjkob9++nf379zN16lRCQkKIj4/ns88+Y+rUqcVXzLNnz2bQoEFmz3QeO3YsR44cITU11aK2rF+/nlOnTjFhwoRy0+fNm8fly5c5ePCg1UH52Wef5dq1a8WT0ZKSkmjZsiWdOnWyqjwhhBC1S7UG5dmzZ/PEE0/QtWvX4mOvv/46I0eO5Pnnn2fdunVs27aNqKgos8t84IEH6N69O1999ZXZ59y4cYNp06YxcuRIfHx8ys3TrFkzFixYQOPGja2+svX09KRPnz6sWbMGkPvJQgghSqu2oJyRkUFCQkKZgOvi4sKSJUto27YtgwcP5tFHH7V4P+GxY8eyZs2a266gVdL8+fPJzs4mOjr6tvmGDRvG2bNnadCggUXtKWno0KFs2LCBK1eu8OOPP8rQtRBCiGLVFpTnzJmDv78/YWFhZdLuuusuYmJi8PPz4/3337f4SnLYsGHcuHGDmJiYSvNmZ2fz4YcfMmPGDLMmb9n6LHFERAQ3btxg9uzZXLhwQYKyEEKIYtUSlFNSUli1ahVRUVEVBlwfHx8OHTrEE088YXH5jRs35rnnnmPp0qVl0hYsWEB4eDjx8fEYDAamTZuGl5cXb775psX1WKNJkyaEh4fzySef0KxZM/z8/BxSrxBCCOfn8KC8ZcsW+vbty3PPPceQIUPsVs9rr71GSkoKBw4cKD525coV3nvvPf71r38xcOBAOnfuzNdff83cuXOpV6+e3dpyq6FDh5KXl1f87LIQQggBDg7KCQkJDBw4kJEjR7Jy5Urc3NzsVtdjjz1GQEAACxYsKD7217/+lfz8fFJTU/n555959NFHGTduHAMHDrRbO8rz9NNPU69ePUJDQx1arxBCCOfm0MWW33rrLaKiooiOjrb7FaKLiwuTJk0iMjKSWbNm0aRJEz799FPGjx+Ph4cHHh4efPnll3ZtQ0U8PDzYs2cPHTt2rJb6hRBCOCezgrJSahbQAzgGvKS1vmk67gYsAzoA+7TWt70xu2jRIiIjI21qsCWGDh3K1KlTWb58OW3btuXkyZNMnjzZYfXfTsnHwIQQQggwY/haKdUNaK21DgZ+AQaXSB4I/MuUdo9S6rHbleXo4dq77rqLyMhIFi1axCeffMILL7xQ4XPIQgghRHUz555yD2CL6XUC0NPMNKfw6quvkp2dzYEDByxahEQIIYRwNHOGr5sA2abXl4Cmt6TlVJAGgFJqPDAeYMyYMVY31BYDBgzgypUr1KtXr8zeyM4oLy+vRrSzOkkfmUf6qXLSR5WTPjJPRf1kyfwhc4LyRaCR6bUHcMHMNAC01l8AXwBkZWUZqmNyU0xMDAaDweaFPxwlKytLJoFVQvrIPNJPlZM+qpz0kXmqop/MGb5OBYp2YHgCSDEzzWm4ubnVmIAshBDizlVpUNZapwFnlFLJwIPAOqVU0VJZG4E/mNLytNb/tF9ThRBCiNrNrMtHrfWtM6QiTcfzgbFV3CYhhBDijlStWzcKIYQQ4r8kKAshhBBOQoKyEEII4SQkKAshhBBOQoKyEEII4SQkKAshhBBOQoKyEEII4SQkKAshhBBOwsVgMFR3G4QQQgiBXCkLIYQQTkOCshBCCOEkJCgLIYQQTkKCshBCCOEkJCgLIYQQTkKCshBCCOEkzNpP2RxKKQ9gK+AHPKq1/kkp9T/As8AVYKzWOtuU1xX4CViktV6olGoDrADqAN9prT+tqnY5E3P7SCm1AngQyAU2aa1nK6WCgSWAp9baq3regWPY2E/9gBmAATgCvKS1LqyO92FPNvbRWGA6cAo4pbUeUR3vwd5s7KMJwFBTUX7AOK31eoe/CQewsZ/ks7t0H9UDPgM6AJe11k8rpToCawBfoJnW+srt6qqyoAxcBQYAs01vwsv09yAgEHgXmGjK+wJwvMS57wDRWusflFJxSql/aK3/VYVtcxaW9NGLWuufSpybYcrzo8NaW31s6acftNbfm85bAfQAdjqm2Q5lSx8BzNdaL3RQW6uL1X2ktV4MLDad9xPGD+Taypb/S/LZXbqPJgHxt3yBOwmEAGZ9qauy4Wut9U2t9dkSh+4FDmmtDcB+IBhAKeUGDMH4zaFIeyDN9DoD4wdprWNuH2G8ylumlNqqlOpmOveS1vqqY1tcPWzspxsASikXU55jjmm1Y9nSRyYTlVLJSqlhDmqyw1VBH6GUCjSdU2t/92zsJ/nsLt1HTwJBSqkdSqlI07lXtdaXzK3LnveUjwLKdDnfB2hqOj4CWAuUHFL8GQhTSrkDjwNN7NguZ1JRH03VWj+G8VvXF9XVOCdiUT+Zhmd/BjyBs9wZLOmj74DOQH9gilKqlaMbW02FsHyOAAAD00lEQVSs+X279QLiTmBJP8lnd+k+8gH2mI4NNw3vW8RuQVlrfQ7j8M8WoB/wi+kq+Xlg9S3ZozHev4kHTgCn7dUuZ1JeH5mOnzf9/AUwmPrtjmVpP2mtV2itH8B4i+SZamm0g1nSR1rri1rrQq31ZWAH8ED1tNqxrPx964fxc+mOYWE/yWd3iT4CLgLbtNb5QCrQydKy7Tr7Wmv9N611CBCL8Zffy/RnE/A/GIfQHtFan9NaD8b45uqa8t4RyukjlFKNTD9bAHW11gXV10LnYG4/mb65FsnBeC/ojmBBHxUdcwO6A79VT4sdz5LfN6WUwjhEea2amlttzO0n+ewu3UdACvCQ6XU34HdLy63KiV4opeJNDeqklFqKcXy9BfD/gNdM92WUKe9YoIHWeo9S6kng/2C8ZzHb9A2+Vqqsj0zZvlFKNQXcgKmm8x4AFgAdlVKJQJTW+oCj2+8o1vYT8KLpPqkLkAVsdGjDHciGPnrLNEvdBViltT7m0IY7kA19BHfQ0LUNn0vy2V26j2YBK5RSHwJbtda/KaWaYLxl2w3YoJT6pGgyanlklyghhBDCScjiIUIIIYSTkKAshBBCOAkJykIIIYSTkKAshBBCOAkJykIIIYSTqNJHooQQ9qGUuo//PvP4J631TNPxL4GXALTWLuWfXWnZfhgX9dmhtd5hOrYCGAMEaq21LW0XQphPgrIQNc9YpdT/AvdgDKa28gPeM73eUQXlCSGsJM8pC1EDlLhS/g1oB4QBbYFFwDmgNcbbUdOBcRjX4tXA61rrQ0qp9zEG3uUY1yhujHFXm72UXXUoFBiL8Ur5LxgX0XAFhmutk+3zDoUQIPeUhahpMoHdGIesX8K4ucRFU9qLwEyMu/VMx7il3HqlVJ0S5wcDCwEP4GOMG3bMM6Wtw7it6s8l8vcAlgFtgPer/N0IIUqRoCxEzfNXjFevPYGvShzvb/o5RWv9Gcb9W9sDHUvkmau1no/xivs+rXUuxvV6AX7SWq/WWv+7RP73tdb/C1wH7qvydyKEKEWCshA1z2qgAOPm6VvLSTfc8rOkC6af+fz39/9297BK5r+jdysTwhEkKAtRw2itczAOXUdqrUvuS77J9HOuUmoS8DTGfV+zKinyP6afwUqpYUqp+lXaYCGE2WT2tRA1kNb6H+UcXoFxwtc4jBPB9mKc6HXTuAthhXYCPwC9TOf5VGljhRBmk9nXQgghhJOQ4WshhBDCSUhQFkIIIZyEBGUhhBDCSUhQFkIIIZyEBGUhhBDCSUhQFkIIIZyEBGUhhBDCSUhQFkIIIZzE/wcgdhZHWo6YTgAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "best_model = TransformerModel.load_from_checkpoint(model_name='air_transformer', best=True)\n",
    "eval_model(best_model, 26, series_scaled, val_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's backtest our `Transformer` model to evaluates its performance at a forecast horizon of 6 months:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=18.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "662c549f7f664f6b9a47f47b7cdd9e80"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "backtest_series = my_model.historical_forecasts(training_series = series_scaled,\n",
    "                                                start = pd.Timestamp('19590101'), \n",
    "                                                forecast_horizon = 6,\n",
    "                                                use_full_output_length = False,\n",
    "                                                retrain = False,\n",
    "                                                verbose = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "MAPE: 6.31%\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 576x360 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "series_scaled.plot(label='actual', lw=2)\n",
    "backtest_series.plot(label='backtest', lw=2)\n",
    "plt.legend()\n",
    "plt.title('Backtest, starting Jan 1959, with a 6-months horizon');\n",
    "print('MAPE: {:.2f}%'.format(mape(scaler.inverse_transform(series_scaled), \n",
    "                                  scaler.inverse_transform(backtest_series))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monthly Sun spots Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's test the transformer architecture on a more complex dataset, the 'monthly sunspots'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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174.723353 \nL 110.266613 185.5494 \nL 110.504144 183.212843 \nL 110.62291 185.471515 \nL 110.860441 180.175319 \nL 110.979206 191.858104 \nL 111.097972 182.823417 \nL 111.216737 184.926319 \nL 111.335503 184.381122 \nL 111.454268 191.702334 \nL 111.573034 189.287892 \nL 111.810565 194.194662 \nL 111.929331 194.817743 \nL 112.048096 191.390793 \nL 112.285627 196.063907 \nL 112.404393 193.72735 \nL 112.641924 196.063907 \nL 112.760689 205.410135 \nL 112.879455 205.254365 \nL 112.99822 207.279381 \nL 113.116986 196.219678 \nL 113.235751 206.96784 \nL 113.473282 204.864939 \nL 113.592048 205.410135 \nL 113.710813 210.316905 \nL 113.829579 208.525545 \nL 114.06711 214.756364 \nL 114.185875 214.756364 \nL 114.304641 211.251528 \nL 114.423406 214.756364 \nL 114.660938 204.241857 \nL 114.779703 204.241857 \nL 114.898469 209.538053 \nL 115.017234 208.525545 \nL 115.136 205.643791 \nL 115.254765 211.095758 \nL 115.492296 205.17648 \nL 115.611062 209.148627 \nL 115.729827 207.590922 \nL 115.848593 214.055397 \nL 115.967358 212.809233 \nL 116.086124 213.198659 \nL 116.204889 208.759201 \nL 116.323655 214.522708 \nL 116.44242 214.600593 \nL 116.561186 214.444823 \nL 116.798717 214.756364 \nL 119.055262 214.756364 \nL 119.174027 209.615938 \nL 119.292793 214.756364 \nL 119.530324 210.005364 \nL 119.649089 214.133282 \nL 119.767855 213.899626 \nL 119.88662 205.955332 \nL 120.124151 214.211167 \nL 120.242917 214.756364 \nL 120.480448 213.743856 \nL 120.599214 214.366937 \nL 120.717979 202.606267 \nL 120.95551 211.718839 \nL 121.193041 206.889955 \nL 121.311807 214.756364 \nL 121.430572 206.734184 \nL 121.549338 213.276544 \nL 121.668103 201.827415 \nL 121.786869 210.472676 \nL 122.0244 200.503366 \nL 122.143165 208.214004 \nL 122.380696 193.104268 \nL 122.618227 203.618775 \nL 122.736993 197.465841 \nL 122.974524 210.316905 \nL 123.093289 196.219678 \nL 123.212055 210.23902 \nL 123.449586 200.347595 \nL 123.568351 212.965003 \nL 124.043414 199.101431 \nL 124.162179 199.802398 \nL 124.280945 189.677318 \nL 124.39971 194.350432 \nL 124.518476 190.144629 \nL 124.637241 207.123611 \nL 124.756007 171.218517 \nL 124.874772 187.107105 \nL 124.993538 177.994533 \nL 125.112303 190.222515 \nL 125.349834 185.783056 \nL 125.4686 164.130961 \nL 125.587365 194.272547 \nL 125.824896 157.354945 \nL 126.062427 180.253204 \nL 126.181193 180.798401 \nL 126.299958 184.536892 \nL 126.418724 196.686989 \nL 126.656255 170.829091 \nL 126.893786 191.468678 \nL 127.012552 186.406138 \nL 127.250083 139.830767 \nL 127.487614 198.244694 \nL 127.725145 175.813746 \nL 127.962676 186.172482 \nL 128.081441 194.817743 \nL 128.200207 192.247531 \nL 128.318972 192.636957 \nL 128.437738 187.574417 \nL 128.556503 197.310071 \nL 128.675269 194.973514 \nL 128.794034 187.885957 \nL 128.9128 173.399304 \nL 129.150331 192.948498 \nL 129.269096 190.222515 \nL 129.387862 194.428317 \nL 129.506627 190.066744 \nL 129.625393 206.266873 \nL 129.862924 189.443662 \nL 130.100455 211.87461 \nL 130.219221 199.023546 \nL 130.337986 199.490858 \nL 130.456752 187.496531 \nL 130.694283 194.428317 \nL 130.813048 203.151464 \nL 130.931814 193.337924 \nL 131.050579 195.20717 \nL 131.169345 190.923482 \nL 131.28811 199.802398 \nL 131.406876 194.038891 \nL 131.525641 211.251528 \nL 131.763172 191.93599 \nL 131.881938 206.344758 \nL 132.119469 194.584088 \nL 132.238234 210.706331 \nL 132.357 207.746692 \nL 132.475765 208.60343 \nL 132.594531 207.201496 \nL 132.713297 198.011038 \nL 132.832062 211.407299 \nL 132.950828 210.316905 \nL 133.069593 207.590922 \nL 133.188359 213.432315 \nL 133.307124 213.354429 \nL 133.42589 212.809233 \nL 133.544655 211.017872 \nL 133.663421 211.329413 \nL 133.782186 200.113939 \nL 134.019717 214.756364 \nL 134.138483 214.756364 \nL 134.257248 214.055397 \nL 134.376014 202.216841 \nL 134.494779 204.241857 \nL 134.613545 213.588085 \nL 134.851076 208.60343 \nL 135.088607 214.756364 \nL 135.207372 214.444823 \nL 135.444903 214.756364 \nL 135.682435 214.756364 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181.343598 \nL 142.095773 172.931992 \nL 142.214538 176.125287 \nL 142.333304 170.206009 \nL 142.570835 178.85127 \nL 142.927131 164.130961 \nL 143.045897 167.168485 \nL 143.283428 138.428833 \nL 143.402193 172.464681 \nL 143.520959 155.252044 \nL 143.639724 175.502205 \nL 143.877255 170.361779 \nL 144.114786 181.265712 \nL 144.233552 176.281057 \nL 144.471083 140.76539 \nL 144.589848 162.18383 \nL 144.708614 157.199175 \nL 144.82738 144.03657 \nL 144.946145 153.772224 \nL 145.064911 173.632959 \nL 145.183676 170.206009 \nL 145.302442 162.105945 \nL 145.539973 174.100271 \nL 145.896269 131.341277 \nL 146.015035 163.118453 \nL 146.1338 164.053075 \nL 146.252566 180.564745 \nL 146.490097 166.389632 \nL 146.608862 149.021225 \nL 146.727628 151.513553 \nL 146.846393 150.812585 \nL 146.965159 177.760877 \nL 147.083924 175.735861 \nL 147.20269 142.011554 \nL 147.440221 185.082089 \nL 147.558986 188.742695 \nL 147.796518 171.997369 \nL 147.915283 185.237859 \nL 148.034049 178.773385 \nL 148.152814 180.876286 \nL 148.27158 192.247531 \nL 148.390345 190.689826 \nL 148.509111 171.530058 \nL 148.627876 171.841599 \nL 148.746642 193.805235 \nL 148.865407 182.589761 \nL 149.221704 207.824578 \nL 149.340469 208.369774 \nL 149.459235 198.322579 \nL 149.578 203.618775 \nL 149.696766 193.337924 \nL 149.815531 205.955332 \nL 149.934297 203.151464 \nL 150.053062 205.565906 \nL 150.171828 212.575577 \nL 150.290593 204.709168 \nL 150.409359 213.977511 \nL 150.528124 209.304397 \nL 150.64689 210.316905 \nL 150.765656 205.721676 \nL 151.003187 210.161135 \nL 151.121952 207.045725 \nL 151.240718 210.939987 \nL 151.359483 200.659136 \nL 151.597014 213.66597 \nL 151.71578 207.902463 \nL 151.834545 208.681315 \nL 151.953311 207.980348 \nL 152.072076 211.640954 \nL 152.547138 187.885957 \nL 152.665904 208.914971 \nL 152.784669 195.674481 \nL 152.903435 199.412972 \nL 153.0222 166.856944 \nL 153.259731 188.898466 \nL 153.378497 168.180993 \nL 153.497262 168.804075 \nL 153.616028 136.248046 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211.87461 \nL 166.323939 196.141792 \nL 166.442704 209.382282 \nL 166.56147 198.011038 \nL 166.680235 206.422643 \nL 167.036532 180.798401 \nL 167.155297 181.032057 \nL 167.274063 170.439665 \nL 167.630359 190.923482 \nL 167.749125 189.599433 \nL 167.86789 191.702334 \nL 167.986656 183.057073 \nL 168.105421 184.069581 \nL 168.224187 168.258878 \nL 168.342952 184.614778 \nL 168.699249 160.859781 \nL 168.818014 168.103108 \nL 168.93678 164.053075 \nL 169.055546 178.539729 \nL 169.174311 172.075255 \nL 169.293077 131.341277 \nL 169.411842 171.218517 \nL 169.649373 163.741534 \nL 169.768139 166.000206 \nL 169.886904 179.785893 \nL 170.00567 148.008717 \nL 170.124435 179.941663 \nL 170.361966 148.320258 \nL 170.480732 174.100271 \nL 170.718263 89.205364 \nL 170.837028 74.251399 \nL 171.074559 129.394146 \nL 171.193325 90.840954 \nL 171.31209 127.680671 \nL 171.668387 135.157653 \nL 171.905918 106.340116 \nL 172.024684 111.558427 \nL 172.143449 136.637473 \nL 172.262215 111.636312 \nL 172.38098 125.499884 \nL 172.499746 90.217872 \nL 172.618511 92.7102 \nL 172.856042 139.597112 \nL 172.974808 134.923997 \nL 173.093573 151.980864 \nL 173.212339 151.513553 \nL 173.331104 154.00588 \nL 173.44987 167.012714 \nL 173.568635 141.777898 \nL 173.687401 159.06842 \nL 173.806166 137.104784 \nL 173.924932 139.207685 \nL 174.043697 154.00588 \nL 174.162463 145.126963 \nL 174.281228 150.423159 \nL 174.399994 180.408975 \nL 174.637525 160.236699 \nL 174.75629 184.303237 \nL 174.993822 147.619291 \nL 175.231353 172.075255 \nL 175.350118 168.025222 \nL 175.587649 132.665326 \nL 175.82518 170.751206 \nL 176.062711 165.532895 \nL 176.181477 186.639794 \nL 176.419008 161.872289 \nL 176.537773 166.078092 \nL 176.656539 175.112779 \nL 176.775304 159.146306 \nL 177.131601 167.0906 \nL 177.250366 163.81942 \nL 177.606663 182.044565 \nL 177.844194 185.5494 \nL 177.96296 162.3396 \nL 178.200491 179.396467 \nL 178.319256 182.745532 \nL 178.438022 181.343598 \nL 178.556787 185.39363 \nL 178.675553 177.682992 \nL 178.794318 187.730187 \nL 179.150615 175.502205 \nL 179.26938 188.66481 \nL 179.388146 181.810909 \nL 179.625677 196.531219 \nL 179.744442 202.762037 \nL 180.100739 194.194662 \nL 180.575801 202.450496 \nL 180.694566 197.310071 \nL 180.813332 204.864939 \nL 180.932098 192.792727 \nL 181.288394 205.877447 \nL 181.40716 201.204333 \nL 181.525925 211.329413 \nL 181.644691 207.668807 \nL 181.882222 214.444823 \nL 182.000987 212.341921 \nL 182.119753 214.756364 \nL 182.238518 207.201496 \nL 182.476049 212.341921 \nL 182.594815 214.366937 \nL 182.71358 210.939987 \nL 182.832346 214.444823 \nL 182.951111 209.693823 \nL 183.069877 214.756364 \nL 183.188642 210.862102 \nL 183.307408 211.173643 \nL 183.426173 210.161135 \nL 183.544939 211.329413 \nL 183.663704 211.251528 \nL 183.78247 208.759201 \nL 183.901235 209.148627 \nL 184.020001 204.086086 \nL 184.257532 210.706331 \nL 184.376298 206.111103 \nL 184.495063 192.013875 \nL 184.613829 202.294726 \nL 184.732594 197.465841 \nL 184.85136 201.593759 \nL 184.970125 181.733024 \nL 185.088891 183.134958 \nL 185.207656 190.3004 \nL 185.445187 184.381122 \nL 185.563953 187.574417 \nL 185.682718 169.972353 \nL 185.801484 184.926319 \nL 186.039015 180.097434 \nL 186.15778 170.595435 \nL 186.276546 171.685828 \nL 186.514077 143.725029 \nL 186.632842 174.333926 \nL 186.989139 146.528897 \nL 187.107905 144.425996 \nL 187.22667 148.008717 \nL 187.345436 143.880799 \nL 187.464201 146.918324 \nL 187.939263 125.499884 \nL 188.176794 151.669323 \nL 188.29556 151.279897 \nL 188.533091 137.727866 \nL 188.651856 159.146306 \nL 188.770622 131.341277 \nL 188.889387 130.172998 \nL 189.008153 123.864294 \nL 189.245684 142.946177 \nL 189.364449 144.581767 \nL 189.483215 138.506718 \nL 189.60198 140.298079 \nL 189.720746 166.233862 \nL 189.958277 136.092276 \nL 190.077043 138.039407 \nL 190.195808 170.51755 \nL 190.314574 146.373127 \nL 190.433339 154.00588 \nL 190.552105 150.501044 \nL 190.67087 152.526061 \nL 190.908401 172.931992 \nL 191.027167 152.058749 \nL 191.145932 165.61078 \nL 191.264698 164.520387 \nL 191.383463 180.798401 \nL 191.620994 164.598272 \nL 191.73976 149.332766 \nL 191.977291 166.078092 \nL 192.096056 162.884797 \nL 192.214822 182.044565 \nL 192.333587 175.346435 \nL 192.452353 182.901302 \nL 192.808649 163.040567 \nL 192.927415 183.134958 \nL 193.046181 172.854107 \nL 193.283712 189.287892 \nL 193.402477 177.293565 \nL 193.521243 197.621612 \nL 193.640008 183.680155 \nL 193.758774 185.39363 \nL 193.877539 182.667647 \nL 193.996305 169.816583 \nL 194.11507 178.072418 \nL 194.233836 163.118453 \nL 194.352601 186.873449 \nL 194.471367 183.134958 \nL 194.590132 169.738698 \nL 194.708898 172.15314 \nL 194.827663 172.075255 \nL 194.946429 192.559072 \nL 195.065194 188.353269 \nL 195.18396 169.894468 \nL 195.302725 192.481186 \nL 195.421491 176.826254 \nL 195.540256 184.147466 \nL 195.659022 183.991696 \nL 195.777787 191.858104 \nL 195.896553 187.885957 \nL 196.015319 188.586925 \nL 196.134084 193.883121 \nL 196.25285 185.315745 \nL 196.490381 201.437988 \nL 196.609146 195.596596 \nL 196.727912 204.787054 \nL 196.965443 184.848433 \nL 197.202974 201.048562 \nL 197.321739 204.709168 \nL 197.440505 201.9053 \nL 197.55927 207.513037 \nL 197.678036 204.864939 \nL 197.796801 209.070741 \nL 197.915567 203.774545 \nL 198.271863 214.756364 \nL 198.390629 214.211167 \nL 198.509394 207.590922 \nL 198.746925 212.497692 \nL 198.865691 213.588085 \nL 198.984456 210.862102 \nL 199.103222 210.939987 \nL 199.340753 204.241857 \nL 199.459519 207.513037 \nL 199.578284 195.129284 \nL 199.69705 202.606267 \nL 199.815815 202.450496 \nL 200.053346 186.250368 \nL 200.172112 193.961006 \nL 200.290877 190.534055 \nL 200.409643 192.481186 \nL 200.647174 180.642631 \nL 200.765939 166.701173 \nL 200.884705 168.72619 \nL 201.00347 162.105945 \nL 201.478532 182.823417 \nL 201.716063 130.328769 \nL 201.834829 168.648304 \nL 201.953594 152.759716 \nL 202.07236 151.980864 \nL 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208.366933 164.754043 \nL 208.604464 189.833088 \nL 208.723229 180.019549 \nL 208.841995 185.004204 \nL 208.96076 161.950174 \nL 209.079526 167.012714 \nL 209.198291 192.948498 \nL 209.317057 188.041728 \nL 209.435822 192.247531 \nL 209.554588 191.93599 \nL 209.673353 203.385119 \nL 209.910884 188.431154 \nL 210.02965 192.09176 \nL 210.148415 205.799562 \nL 210.267181 196.141792 \nL 210.385946 205.020709 \nL 210.504712 203.385119 \nL 210.623477 212.887118 \nL 210.861008 200.970677 \nL 210.979774 207.045725 \nL 211.217305 203.073578 \nL 211.336071 190.45617 \nL 211.454836 212.965003 \nL 211.573602 210.784217 \nL 211.692367 213.5102 \nL 211.811133 202.917808 \nL 211.929898 207.902463 \nL 212.048664 207.045725 \nL 212.167429 203.618775 \nL 212.40496 208.369774 \nL 212.523726 195.752366 \nL 212.642491 207.980348 \nL 212.880022 202.450496 \nL 212.998788 198.244694 \nL 213.236319 210.161135 \nL 213.355084 209.849594 \nL 213.47385 201.983185 \nL 213.592615 209.538053 \nL 213.711381 203.463005 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160.781896 \nL 219.887188 162.18383 \nL 220.005953 140.142308 \nL 220.243485 179.552237 \nL 220.36225 179.396467 \nL 220.481016 183.290729 \nL 220.837312 149.021225 \nL 220.956078 182.200335 \nL 221.074843 167.557911 \nL 221.312374 181.421483 \nL 221.43114 150.812585 \nL 221.549905 189.755203 \nL 221.787436 151.980864 \nL 221.906202 178.929155 \nL 222.024967 173.78873 \nL 222.143733 149.488536 \nL 222.262498 148.94334 \nL 222.381264 155.64147 \nL 222.500029 143.491373 \nL 222.618795 147.074094 \nL 222.73756 147.151979 \nL 223.093857 174.879123 \nL 223.212623 173.399304 \nL 223.331388 171.296402 \nL 223.450154 166.545403 \nL 223.687685 186.250368 \nL 223.80645 177.994533 \nL 223.925216 181.421483 \nL 224.043981 158.834765 \nL 224.162747 175.969516 \nL 224.281512 171.919484 \nL 224.519043 149.566422 \nL 224.87534 183.91381 \nL 224.994105 184.614778 \nL 225.112871 188.82058 \nL 225.231636 197.855268 \nL 225.350402 191.468678 \nL 225.469167 194.584088 \nL 225.587933 170.128124 \nL 225.944229 193.649465 \nL 226.062995 191.157137 \nL 226.181761 201.593759 \nL 226.300526 198.088923 \nL 226.538057 214.522708 \nL 226.656823 205.098594 \nL 226.775588 206.734184 \nL 226.894354 204.475513 \nL 227.013119 211.485184 \nL 227.131885 209.382282 \nL 227.25065 199.179317 \nL 227.369416 202.528382 \nL 227.488181 196.609104 \nL 227.606947 198.088923 \nL 227.725712 208.992856 \nL 227.844478 209.615938 \nL 227.963243 209.382282 \nL 228.082009 198.63412 \nL 228.31954 209.226512 \nL 228.438305 208.681315 \nL 228.557071 210.784217 \nL 228.675836 209.304397 \nL 228.794602 209.226512 \nL 229.032133 212.575577 \nL 229.150898 207.902463 \nL 229.269664 213.120774 \nL 229.38843 206.422643 \nL 229.625961 214.133282 \nL 229.744726 208.136119 \nL 229.982257 211.407299 \nL 230.101023 212.887118 \nL 230.338554 207.201496 \nL 230.457319 198.712005 \nL 230.69485 213.120774 \nL 230.813616 214.600593 \nL 230.932381 209.538053 \nL 231.051147 210.628446 \nL 231.169912 214.289052 \nL 231.288678 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236.989423 174.022386 \nL 237.226954 135.936505 \nL 237.345719 137.727866 \nL 237.464485 132.198014 \nL 237.702016 163.429994 \nL 237.820781 155.953011 \nL 237.939547 170.67332 \nL 238.295844 162.417485 \nL 238.414609 167.24637 \nL 238.533375 154.862618 \nL 238.65214 162.18383 \nL 238.770906 159.06842 \nL 238.889671 177.527221 \nL 239.008437 161.093436 \nL 239.127202 169.816583 \nL 239.245968 161.872289 \nL 239.364733 177.994533 \nL 239.483499 159.691502 \nL 239.602264 192.169645 \nL 239.72103 170.050239 \nL 239.958561 180.642631 \nL 240.077326 193.182153 \nL 240.196092 176.592598 \nL 240.314857 179.708008 \nL 240.433623 193.57158 \nL 240.552388 167.012714 \nL 240.671154 192.636957 \nL 240.908685 181.577253 \nL 241.02745 183.134958 \nL 241.146216 191.858104 \nL 241.264982 192.09176 \nL 241.383747 190.611941 \nL 241.621278 205.955332 \nL 241.740044 193.260039 \nL 241.858809 197.777382 \nL 241.977575 177.293565 \nL 242.215106 208.214004 \nL 242.333871 188.82058 \nL 242.452637 191.235023 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "df2 = pd.read_csv('monthly-sunspots.csv', delimiter=\",\")\n",
    "series_sunspot = TimeSeries.from_dataframe(df2, 'Month', ['Sunspots'])\n",
    "\n",
    "series_sunspot.plot()\n",
    "check_seasonality(series_sunspot, max_lag=240)\n",
    "\n",
    "train_sp, val_sp = series_sunspot.split_after(pd.Timestamp('19401001'))\n",
    "\n",
    "scaler_sunspot = Scaler()\n",
    "train_sp_scaled = scaler_sunspot.fit_transform(train_sp)\n",
    "val_sp_scaled = scaler_sunspot.transform(val_sp)\n",
    "series_sp_scaled = scaler_sunspot.transform(series_sunspot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "\"the 'monthly sun spots' dataset has 2820 data points\""
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "'the \\'monthly sun spots\\' dataset has {} data points'.format(df2.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's perform one-step ahead forecasting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_EPOCHS = 50\n",
    "NR_EPOCHS_VALIDATION_PERIOD = 5\n",
    "\n",
    "# Number of previous time stamps taken into account.\n",
    "SEQ_LENGTH = 125\n",
    "# number of output time-steps to predict\n",
    "OUTPUT_LEN = 1\n",
    "# Number of layers in encoder/decoder\n",
    "NUM_LAYERS = 6\n",
    "\n",
    "my_model_sp = TransformerModel(\n",
    "    batch_size = 32,\n",
    "    input_length = SEQ_LENGTH,\n",
    "    input_size = 1,\n",
    "    output_length = OUTPUT_LEN,\n",
    "    output_size = 1,\n",
    "    n_epochs = N_EPOCHS,\n",
    "    model_name = 'sun_spots_transformer',\n",
    "    log_tensorboard=True,\n",
    "    nr_epochs_val_period = NR_EPOCHS_VALIDATION_PERIOD,\n",
    "    model = None,\n",
    "    d_model = 64,\n",
    "    nhead = 32,\n",
    "    num_encoder_layers = 6,\n",
    "    num_decoder_layers = 6,\n",
    "    dim_feedforward = 2048,\n",
    "    dropout = 0.1,\n",
    "    activation = \"relu\",\n",
    "    custom_encoder = None,\n",
    "    custom_decoder = None,\n",
    "    random_state=42,\n",
    "    optimizer_kwargs={'lr': 1e-4}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=50.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "b857c8e60cbe47ae8dbaf1360d6d5f84"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "my_model_sp.fit(training_series=train_sp_scaled, val_training_series=val_sp_scaled, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "loading model_best_15.pth.tar\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "7c297b04116243c092c683eb48c6f0b7"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "85bbcf96798845a5bb02cb5761ab22e1"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nTransformer MAPE: 797.8750218172952\nETS MAPE: 593.7634916506821\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# this function is used to backtest the model at a forecasting horizon of three years (36 months)\n",
    "def backtest(testing_model):\n",
    "    # Compute the backtest predictions with the two models\n",
    "    pred_series = testing_model.historical_forecasts(training_series = series_sp_scaled, \n",
    "                                                     start = pd.Timestamp('19401001'), \n",
    "                                                     forecast_horizon = 36,\n",
    "                                                     stride = 10,\n",
    "                                                     retrain = False,\n",
    "                                                     verbose = True,\n",
    "                                                     use_full_output_length = True)\n",
    "    \n",
    "    pred_series_ets = ExponentialSmoothing().historical_forecasts(training_series = series_sp_scaled,\n",
    "                                                                  start = pd.Timestamp('19401001'), \n",
    "                                                                  forecast_horizon = 36,\n",
    "                                                                  stride = 10,\n",
    "                                                                  retrain = True,\n",
    "                                                                  verbose = True)\n",
    "    val_sp_scaled.plot(label = 'actual')\n",
    "    pred_series.plot(label = 'our Transformer')\n",
    "    pred_series_ets.plot(label = 'ETS')\n",
    "    plt.legend();\n",
    "    print(\"Transformer MAPE:\", mape(pred_series, val_sp_scaled))\n",
    "    print(\"ETS MAPE:\", mape(pred_series_ets, val_sp_scaled))\n",
    "    \n",
    "best_model_sp = TransformerModel.load_from_checkpoint(model_name='sun_spots_transformer', best=True)\n",
    "backtest(best_model_sp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about multi-step forecasting on the next three years? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_EPOCHS = 200\n",
    "NR_EPOCHS_VALIDATION_PERIOD = 5\n",
    "\n",
    "# Number of previous time stamps taken into account.\n",
    "SEQ_LENGTH = 125\n",
    "# number of output time-steps to predict\n",
    "OUTPUT_LEN = 36\n",
    "# Number of layers in encoder/decoder\n",
    "NUM_LAYERS = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_model_sp_long = TransformerModel(\n",
    "    batch_size = 32,\n",
    "    input_length = SEQ_LENGTH,\n",
    "    input_size = 1,\n",
    "    output_length = OUTPUT_LEN,\n",
    "    output_size = 1,\n",
    "    n_epochs = N_EPOCHS,\n",
    "    model_name = 'sun_spots_transformer_long',\n",
    "    log_tensorboard=True,\n",
    "    nr_epochs_val_period = NR_EPOCHS_VALIDATION_PERIOD,\n",
    "    model = None,\n",
    "    d_model = 64,\n",
    "    nhead = 32,\n",
    "    num_encoder_layers = 6,\n",
    "    num_decoder_layers = 6,\n",
    "    dim_feedforward = 2048,\n",
    "    dropout = 0.1,\n",
    "    activation = \"relu\",\n",
    "    custom_encoder = None,\n",
    "    custom_decoder = None,\n",
    "    random_state=42,\n",
    "    optimizer_kwargs={'lr': 1e-4}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "211cf7a106bf4670b275d8315068ec54"
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
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   "source": [
    "my_model_sp_long.fit(training_series=train_sp_scaled, val_training_series=val_sp_scaled, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "loading model_best_185.pth.tar\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))",
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       "model_id": "0bf7dbec05b4470486e84b155173004f"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))",
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     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nTransformer MAPE: 66.44409793467437\nETS MAPE: 593.7634916506821\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "best_model_sp_long = TransformerModel.load_from_checkpoint(model_name='sun_spots_transformer_long', best=True)\n",
    "backtest(best_model_sp_long)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}